title:
What happens to spin during the SO(3)->SE(2) contraction? (On spin and
  extended structures in quantum mechanics)

abstract:
  It is shown that the spin operator can be described by an algebra which is in
between so(3) and e(2). Relativistic version of the singlet state for two Dirac
electrons is discussed. It is shown that a measure of massless particle's
extension can be naturally constructed and that this measure corresponds at the
classical level to the radius of the Robinson congruence.


title: Effective Quantum Observables

abstract:
  Thought experiments about the physical nature of set theoretical
counterexamples to the axiom of choice motivate the investigation of peculiar
constructions, e.g. an infinite dimensional Hilbert space with a modular
quantum logic. Applying a concept due to BENIOFF, we identify the intrinsically
effective Hamiltonians with those observables of quantum theory which may
coexist with a failure of the axiom of choice. Here a self adjoint operator is
intrinsically effective, iff the Schroedinger equation of its generated
semigroup is soluble by means of eigenfunction series expansions.


title: Nonlocal effects in Fock space

abstract:
  If a physical system contains a single particle, and if two distant detectors
test the presence of linear superpositions of one-particle and vacuum states, a
violation of classical locality can occur. It is due to the creation of a
two-particle component by the detecting process itself.


title: An optical method for teleportation

abstract:
  A teleportation method using standard present day optical technology is
presented.


title: Effect of Decoherence on Bell's Inequality for an EPR Pair

abstract:
  According to Bell's theorem, the degree of correlation between spatially
separated measurements on a quantum system is limited by certain inequalities
if one assumes the condition of locality. Quantum mechanics predicts that this
limit can be exceeded, making it nonlocal. We analyse the effect of an
environment modelled by a fluctuating magnetic field on the quantum
correlations in an EPR singlet as seen in the Bell inequality. We show that in
an EPR setup, the system goes from the usual 'violation' of Bell inequality to
a 'non-violation' for times larger than a characteristic time scale which is
related to the parameters of the fluctuating field. We also look at these
inequalities as a function of the spatial separation between the EPR pair.


title: Analysis of the Stern-Gerlach Measurement

abstract:
  A dynamical model for the collapse of the wave function in a quantum
measurement process is proposed by considering the interaction of a quantum
system (spin-1/2) with a macroscopic quantum apparatus interacting with an
environment in a dissipative manner. The dissipative interaction leads to
decoherence in the superposition states of the apparatus, making its behaviour
classical in the sense that the density matrix becomes diagonal with time.
Since the apparatus is also interacting with the system, the probabilities of
the diagonal density matrix are determined by the state vector of the system.
We consider a Stern-Gerlach type model, where a spin- 1/2 particle is in an
inhomogeneous magnetic field, the whole set up being in contact with a large
environment. Here we find that the density matrix of the combined system and
apparatus becomes diagonal and the momentum of the particle becomes correlated
with a spin operator, selected by the choice of the system-apparatus
interaction. This allows for a measurement of spin via a momentum measurement
on the particle with associated probabilities in accordance with quantum
principles.


title: Interaction with a pre and post selected environment and recoherence

abstract:
  The interaction of an open system $\s$ with a pre- and post-selected
environment is studied. In general, under such circumstances $\s$ can not be
described in terms of a density matrix, {\it even when $\s$ in not
post-selected}. However, a simple description in terms of a two-state (TS) is
always available. The two-state of $\s$ evolves in time from an initially
`pure' TS to a `mixed' TS and back to a final `pure' TS. This generic process
is governed by a modified Liouville equation, which is derived. For a sub-class
of observables, which can still be described by an ordinary density matrix,
this evolution generates recoherence to a final pure state. In some cases
post-selection can even suppress any decoherence.


title:
Optimal Measurements of Magnetic Flux in Superconducting Circuits and
  Macroscopic Quantum Mechanics

abstract:
  A model of repeated quantum measurements of magnetic flux in superconducting
circuits manifesting tunneling is discussed. The perturbation due to the
previous measurements of magnetic flux is always present unless quantum
nondemolition measurements are performed. By replacing the classical notion of
noninvasivity with this condition, temporal Bell-like inequalities allows one
to test the observability at the macroscopic level of the conflict between
realism and quantum theory.


title: Cannot Local Reality Exist in the EPR-Bohm Gedankenexperiment ?

abstract:
  We model measuring processes of a single spin-1/2 object and of a pair of
spin-1/2 objects in the EPR-Bohm state by systems of differential equations.
Our model is a local model with hidden-variables of the EPR-Bohm
Gedankenexperiment. Although there is no dynamical interaction between a pair
of spin-1/2 objects, the model can reproduce approximately the
quantum-mechanical correlations by the coincidence counting. Hence the Bell
inequality is violated. This result supports the idea that the coincidence
counting is the source of the non-locality in the EPR-Bohm Gedankenexperiment.


title:
Conditional probabilities in quantum theory, and the tunneling time
  controversy

abstract:
  It is argued that there is a sensible way to define conditional probabilities
in quantum mechanics, assuming only Bayes's theorem and standard quantum
theory. These probabilities are equivalent to the ``weak measurement''
predictions due to Aharonov {\it et al.}, and hence describe the outcomes of
real measurements made on subensembles. In particular, this approach is used to
address the question of the history of a particle which has tunnelled across a
barrier. A {\it gedankenexperiment} is presented to demonstrate the physically
testable implications of the results of these calculations, along with graphs
of the time-evolution of the conditional probability distribution for a
tunneling particle and for one undergoing allowed transmission. Numerical
results are also presented for the effects of loss in a bandgap medium on
transmission and on reflection, as a function of the position of the lossy
region; such loss should provide a feasible, though indirect, test of the
present conclusions. It is argued that the effects of loss on the pulse {\it
delay time} are related to the imaginary value of the momentum of a tunneling
particle, and it is suggested that this might help explain a small discrepancy
in an earlier experiment.


title: IS THERE A CLASSICAL ANALOG OF A QUANTUM TIME-TRANSLATION MACHINE?

abstract:
  In a recent article [D. Suter, Phys. Rev. {\bf A 51}, 45 (1995)] Suter has
claimed to present an optical implementation of the quantum time-translation
machine which ``shows all the features that the general concept predicts and
also allows, besides the quantum mechanical, a classical description.'' It is
argued that the experiment proposed and performed by Suter does not have the
features of the quantum time-translation machine and that the latter has no
classical analog.


title: Bell's inequalities and density matrices. Revealing hidden nonlocality.

abstract:
  As is well known, quantum mechanical behavior cannot, in general, be
simulated by a local hidden variables model. Most -if not all- the proofs of
this incompatibility refer to the correlations which arise when each of two (or
more) systems separated in space is subjected to a single ideal measurement.
This setting is good enough to show contradictions between local hidden
variables models and quantum mechanics in the case of pure states. However, as
shown here, it is not powerful enough in the case of mixtures. This is
illustrated by an example. In this example, the correlations which arise when
each of two systems separated in space is subjected to a single ideal
measurement are classical; only when each system is subjected to a {\it
sequence} of ideal measurements non-classical correlations are obtained. We
also ask whether there are situations for which even this last procedure is not
powerful enough and non-ideal measurements have to be considered as well.


title: Dissipation and memory capacity in the quantum brain model

abstract:
  The quantum model of the brain proposed by Ricciardi and Umezawa is extended
to dissipative dynamics in order to study the problem of memory capacity. It is
shown that infinitely many vacua are accessible to memory printing in a way
that in sequential information recording the storage of a new information does
not destroy the previously stored ones, thus allowing a huge memory capacity.
The mechanism of information printing is shown to induce breakdown of
time-reversal symmetry. Thermal properties of the memory states as well as
their relation with squeezed coherent states are finally discussed.


title:
Quantum Electrodynamics at Large Distances III: Verification of Pole
  Factorization and the Correspondence Principle

abstract:
  In two companion papers it was shown how to separate out from a scattering
function in quantum electrodynamics a distinguished part that meets the
correspondence-principle and pole-factorization requirements. The integrals
that define the terms of the remainder are here shown to have singularities on
the pertinent Landau singularity surface that are weaker than those of the
distinguished part. These remainder terms therefore vanish, relative to the
distinguished term, in the appropriate macroscopic limits. This shows, in each
order of the perturbative expansion, that quantum electrodynamics does indeed
satisfy the pole-factorization and correspondence-principle requirements in the
case treated here. It also demonstrates the efficacy of the computational
techniques developed here to calculate the consequences of the principles of
quantum electrodynamics in the macroscopic and mesoscopic regimes.


title:
Consistent use of paradoxes in deriving constraints on the dynamics of
  physical systems and of no-go-theorems

abstract:
  The classical methods used by recursion theory and formal logic to block
paradoxes do not work in quantum information theory. Since quantum information
can exist as a coherent superposition of the classical ``yes'' and ``no''
states, certain tasks which are not conceivable in the classical setting can be
performed in the quantum setting. Classical logical inconsistencies do not
arise, since there exist fixed point states of the diagonalization operator. In
particular, closed timelike curves need not be eliminated in the quantum
setting, since they would not lead to any paradoxical outcome controllability.
Quantum information theory can also be subjected to the treatment of
inconsistent information in databases and expert systems. It is suggested that
any two pieces of contradicting information are stored and processed as
coherent superposition. In order to be tractable, this strategy requires
quantum computation.


title: Roentgen term makes dipole approximation more divergent

abstract:
  The Roentgen correction to the dipole interaction term leads to an additional
divergency which can be eliminated for infinitely heavy atoms. For M < infinity
a probability of emission in a given direction is represented by a divergent
integral.


title:
INTRINSIC MECHANISM FOR ENTROPY CHANGE IN CLASSICAL AND QUANTUM
  EVOLUTION

abstract:
  It is shown that the existence of a time operator in the Liouville space
representation of both classical and quantum evolution provides a mechanism for
effective entropy change of physical states. In particular, an initially
effectively pure state can evolve under the usual unitary evolution to an
effectively mixed state.


title: Is Mental Process Non-Computable?

abstract:
  It has recently been claimed that certain aspects of mental processing cannot
be simulated by computers, even in principle. The argument is examined and a
lacuna is identified.


title:
Why Classical Mechanics Cannot Naturally Accommodate Consciousness But
  Quantum Mechanics Can.

abstract:
  It is argued on the basis of certain mathematical characteristics that
classical mechanics is not constitutionally suited to accomodate consciousness,
whereas quantum mechanics is. These mathematical characteristics pertain to the
nature of the information represented in the state of the brain, and the way
this information enters into the dynamics.


title: Intrinsic and operational observables in quantum mechanics

abstract:
  The concept of intrinsic and operational observables in quantum mechanics is
introduced. In any realistic description of a quantum measurement that includes
a macroscopic detecting device, it is possible to construct from the statistics
of the recorded raw data a set of operational quantities that correspond to the
intrinsic quantum mechanical observable.


title:
A FAMILY OF NONLINEAR SCHR\"ODINGER EQUATIONS: LINEARIZING
  TRANSFORMATIONS AND RESULTING STRUCTURE

abstract:
  We examine a recently-proposed family of nonlinear Schr\"odinger equations
[J. Phys. A: Math. Gen. 27:1771(1994)] with respect to a group of
transformations that linearize a subfamily of them. We investigate the
structure of the whole family with respect to the linearizing transformations,
and propose a new, invariant parameterization.


title:
Interpretation of the evolution parameter of the Feynman parametrization
  of the Dirac equation

abstract:
  The Feynman parametrization of the Dirac equation is considered in order to
obtain an indefinite mass formulation of relativistic quantum mechanics. It is
shown that the parameter that labels the evolution is related to the proper
time. The Stueckelberg interpretation of antiparticles naturally arises from
the formalism.


title: THE "FREELY" FALLING TWO-LEVEL ATOM IN A RUNNING LASER WAVE

abstract:
  The time evolution of a two-level atom which is simultaneously exposed to the
field of a running laser wave and a homogeneous gravitational field is studied.
The result of the coupled dynamics of internal transitions and center-of-mass
motion is worked out exactly. Neglecting spontaneous emission and performing
the rotating wave approximation we derive the complete time evolution operator
in an algebraical way by using commutation relations. The result is discussed
with respect to the physical implications. In particular the long time and
short time behaviour is physically analyzed in detail. The breakdown of the
Magnus perturbation expansion is shown.


title: Nonlocal and local ghost fields in quantum correlations.

abstract:
  Einstein Podolsky Rosen quantum correlations are discussed from the
perspective of a ghost field introduced by Einstein. The concepts of ghost
field, hidden variables, local reality and the Bell inequality are reviewed. In
the framework of the correlated singlet state, it is shown that quantum
mechanics can be cast in a way that has the form of either nonpositive and
local ghost field or a positive and nonlocal ghost field.


title:
Scaling property of variational perturbation expansion for general
  anharmonic oscillator

abstract:
  We prove a powerful scaling property for the extremality condition in the
recently developed variational perturbation theory which converts divergent
perturbation expansions into exponentially fast convergent ones. The proof is
given for the energy eigenvalues of an anharmonic oscillator with an arbitrary
$x^p$-potential. The scaling property greatly increases the accuracy of the
results.


title:
Variational perturbation expansion for strong-coupling coefficients of
  the anharmonic oscillator

abstract:
  As an application of a recently developed variational perturbation theory we
find the first 22 terms of the convergent strong-coupling series expansion for
the ground state energy of the quartic anharmonic oscillator.


title: Quantum Cryptography with Coherent States

abstract:
  The safety of a quantum key distribution system relies on the fact that any
eavesdropping attempt on the quantum channel creates errors in the
transmission. For a given error rate, the amount of information that may have
leaked to the eavesdropper depends on both the particular system and the
eavesdropping strategy. In this work, we discuss quantum cryptographic
protocols based on the transmission of weak coherent states and present a new
system, based on a symbiosis of two existing ones, and for which the
information available to the eavesdropper is significantly reduced. This system
is therefore safer than the two previous ones. We also suggest a possible
experimental implementation.


title: Quantum Cryptography Based on Orthogonal States

abstract:
  All existing quantum cryptosystems use non-orthogonal states as the carriers
of information. Non-orthogonal states cannot be cloned (duplicated) by an
eavesdropper. In result, any eavesdropping attempt must introduce errors in the
transmission, and therefore, can be detected by the legal users of the
communication channel. Orthogonal states are not used in quantum cryptography,
since they can be faithfully cloned without altering the transmitted data. In
this Letter we present a cryptographic scheme based on orthogonal states, which
also assures the detection of any eavesdropper.


title:
Relativistic Quantization and Improved Equation for a Free Relativistic
  Particle

abstract:
  Usually the only difference between relativistic quantization and standard
one is that the Lagrangian of the system under consideration should be Lorentz
invariant. The standard approaches are logically incomplete and produce
solutions with unpleasant properties: negative-energy, superluminal propagation
etc. We propose a two-projections scheme of (special) relativistic
quantization. The first projection defines the quantization procedure (e.g. the
Berezin-Toeplitz quantization). The second projection defines a casual
structure of the relativistic system (e.g. the operator of multiplication by
the characteristic function of the future cone). The two-projections
quantization introduces in a natural way the existence of three types of
relativistic particles (with $0$, $\frac{1}{2}$, and $1$ spins). Keywords:
Quantization, relativity, spin, Dirac equation, Klein-Gordon equation,
electron, Segal-Bargmann space, Berezin-Toeplitz quantization. AMSMSC Primary:
81P10, 83A05; Secondary: 81R30, 81S99, 81V45


title:
Quantum Oscillator with Kronig-Penney Excitation in Different Regimes of
  Damping

abstract:
  There are discussed the exact solution of the time--dependent Schr\"{o}dinger
equation for a damped quantum oscillator subject to a periodical frequency
delta--kicks describing squeezed states which are expressed in terms of
Chebyshev polynomials. The cases of strong and weak damping are investigated in
the frame of Caldirola--Kanai model.


title:
Deformation of Partical Distribution Functions due to Q-nonlinearity and
  Nonstationary Casimir Effect

abstract:
  The geometrical phase is shown to be integral of motion. Deformation of
particle distribution function corresponding to nonstationary Casimir effect is
expressed in terms of multivariable Hermite polynomials. Correction to Planck
distribution due to q--nonlinearity is discussed.


title:
Husimi Parametric Oscillator in Frame of Symplectic Group and
  Q-oscillators

abstract:
  Time--dependent integrals of motion which are linear forms in position and
momentum are discussed for Husimi parametric forced oscillator. Generalization
of these integrals of motion for q--oscillator is presented. Squeezing and
quadrature correlation phenomena are discussed on the base of Schr\"odinger
uncertainty relation. The properties of the generalized correlated states,
squeezed states, even and odd coherent states (the Schr\"odinger cat states)
are reviewed. The relation of the constructed nonclassical states to
representations of the symplectic symmetry group and finite symmetry groups is
discussed.


title: Photon Statistics for MUltimode Squeezed Schr\"odinger Cat States

abstract:
  Particle distributions in squeezed states, even and odd coherent states are
given in terms of multivariable Hermite polynomials. The Q--function and Wigner
function for nonclassical field states are discussed.


title:
Decay Rates of Metastable States in Cubic Potential by Variational
  Perturbation Theory

abstract:
  Variational perturbation theory is used to determine the decay rates of
metastable states across a cubic barrier of arbitrary height. For high
barriers, a variational resummation procedure is applied to the complex energy
eigenvalues obtained from a WKB expansion; for low barriers, the variational
resummation procedure converts the non-Borel-summable
Rayleigh-Schr\"o\-din\-ger expansion into an exponentially fast convergent one.
The results in the two regimes match and yield very accurate imaginary parts of
the energy eigenvalues. This is demonstrated by comparison with the complex
eigenvalues from solutions of the Schr\"odinger equation via the
complex-coordinate rotation method.


title: Classical and quantum Malus' law

abstract:
  The classical and the quantum Malus' Laws for light and spin are discussed.
It is shown that for spin-1/2, the quantum Malus' Law is equivalent in form to
the classical Malus' Law provided that the statistical average involves a
quasi-distribution function that can become negative. A generalization of
Malus' Law for arbitrary spin-s is obtained in the form of a Feynman
path-integral representation for the Malus amplitude. The classical limit of
the Malus amplitude for large s is discussed.


title: Quantum chaos: a decoherent definition.

abstract:
  We show that the rate of increase of von Neumann entropy computed from the
reduced density matrix of an open quantum system is an excellent indicator of
the dynamical behavior of its classical hamiltonian counterpart. In decohering
quantum analogs of systems which exhibit classical hamiltonian chaos entropy
production rate quickly tends to a constant which is given by the sum of the
positive Lyapunov exponents, and falls off only as the system approaches
equilibrium. By contrast, integrable systems tend to have entropy production
rate which decreases as $t^{-1}$ well before equilibrium is attained. Thus,
behavior of quantum systems in contact with the environment can be used as a
test to determine the nature of their hamiltonian evolution.


title:
Detecting Casimir Forces through a Tunneling Electromechanical
  Transducer

abstract:
  We propose the use of a tunneling electromechanical transducer to dynamically
detect Casimir forces between two conducting surfaces. The maximum distance for
which Casimir forces should be detectable with our method is around $1 \mu$m,
while the lower limit is given by the ability to approach the surfaces. This
technique should permit to study gravitational forces on the same range of
distances, as well as the vacuum friction provided that very low dissipation
mechanical resonators are used.


title:
Quantum Electrodynamics at Large Distances I: Extracting the
  Correspondence-Principle Part.

abstract:
  The correspondence principle is important in quantum theory on both the
fundamental and practical levels: it is needed to connect theory to experiment,
and for calculations in the technologically important domain lying between the
atomic and classical regimes. Moreover, a correspondence-principle part of the
S-matrix is normally separated out in quantum electrodynamics in order to
obtain a remainder that can be treated perturbatively. But this separation, as
usually performed, causes an apparent breakdown of the correspondence principle
and the associated pole-factorization property. This breakdown is spurious. It
is shown in this article, and a companion, in the context of a special case,
how to extract a distinguished part of the S-matrix that meets the
correspondence-principle and pole-factorization requirements. In a second
companion paper the terms of the remainder are shown to vanish in the
appropriate macroscopic limits. Thus this work validates the correspondence
principle and pole factorization in quantum electrodynamics, in the special
case treated here, and creates a needed computational technique.


title: Comment on 'Quantum Backreaction on "Classical" Variables'

abstract:
  It is argued that the bracket of Anderson's canonical theory should have been
antisymmetric otherwise serious controversies arise like violation of both
hermiticity and the Leibniz rule of differentiation.


title: Quantum Langevin equation from forward--backward path integral

abstract:
  The quantum Langevin equation is derived from the Feynman-Veron
forward--backward path integral representation for a density matrix of a
quantum system in a thermal oscillator bath. We exhibit the mechanism by which
the classical, $c$-valued noise in the Feynman-Vernon theory turns into an
operator-valued quantum noise fulfilling characteristic commutation relation
necessary for the unitarity of the time evolution in the quantum Langevin
equation.


title:
Simple Realization Of The Fredkin Gate Using A Series Of Two-body
  Operators

abstract:
  The Fredkin three-bit gate is universal for computational logic, and is
reversible. Classically, it is impossible to do universal computation using
reversible two-bit gates only. Here we construct the Fredkin gate using a
combination of six two-body reversible (quantum) operators.


title:
A pragmatic approach to the problem of the self-adjoint extension of
  Hamilton operators with the Aharonov-Bohm potential

abstract:
  We consider the problem of self-adjoint extension of Hamilton operators for
charged quantum particles in the pure Aharonov-Bohm potential (infinitely thin
solenoid). We present a pragmatic approach to the problem based on the
orthogonalization of the radial solutions for different quantum numbers. Then
we discuss a model of a scalar particle with a magnetic moment which allows to
explain why the self-adjoint extension contains arbitrary parameters and give a
physical interpretation.


title: Quantum Computers, Factoring, and Decoherence

abstract:
  In a quantum computer any superposition of inputs evolves unitarily into the
corresponding superposition of outputs. It has been recently demonstrated that
such computers can dramatically speed up the task of finding factors of large
numbers -- a problem of great practical significance because of its
cryptographic applications. Instead of the nearly exponential ($\sim \exp
L^{1/3}$, for a number with $L$ digits) time required by the fastest classical
algorithm, the quantum algorithm gives factors in a time polynomial in $L$
($\sim L^2$). This enormous speed-up is possible in principle because quantum
computation can simultaneously follow all of the paths corresponding to the
distinct classical inputs, obtaining the solution as a result of coherent
quantum interference between the alternatives. Hence, a quantum computer is
sophisticated interference device, and it is essential for its quantum state to
remain coherent in the course of the operation. In this report we investigate
the effect of decoherence on the quantum factorization algorithm and establish
an upper bound on a ``quantum factorizable'' $L$ based on the decoherence
suffered per operational step.


title:
Quantum State Diffusion, Density Matrix Diagonalization and Decoherent
  Histories: A Model

abstract:
  We analyse the quantum evolution of a particle moving in a potential in
interaction with an environment of harmonic oscillators in a thermal state,
using the quantum state diffusion (QSD) picture of Gisin and Percival, in which
one associates the usual Markovian master equation for the density operator
with a class of stochastic non-linear Schr\"odinger equations. We find
stationary solutions to the Ito equation which are Gaussians, localized around
a point in phase space undergoing classical Brownian motion. We show that every
initial state approaches these stationary solutions in the long time limit. We
recover the density operator corresponding to these solutions, and thus show,
for this particular model, that the QSD picture effectively supplies a
prescription for approximately diagonalizing the density operator in a basis of
phase space localized states. The rate of localization is related to the
decoherence time, and also to the timescale on which thermal and quantum
fluctuations become comparable. We use these results to exemplify the general
connection between the QSD picture and the decoherent histories approach.


title: Standard Model plus Gravity from Octonion Creators and Annihilators

abstract:
  Octonion creation and annihilation operators are used to construct the
Standard Model plus Gravity. The resulting phenomenological model is the
D4-D5-E6 model described in hep-ph/9501252 .


title: Stronger-than-quantum correlations

abstract:
  After an elementary derivation of Bell's inequality, several forms of
expectation functions for two-valued observables are discussed. Special
emphasis is given to hypothetical stronger-than quantum expectation functions
which give rise to a maximal violation of Bell's inequality.


title:
Polarization Structure of Quantum Light Fields: A New Insight. 2:
  Generalized Coherent States, Squeezing and Geometric Phases

abstract:
  Within the new description of the polarization structure of quantum light
(given in Part I) some types of generalized coherent states related to the
polarization SU(2) group are examined. With their help we give a quasiclassical
description of polarization properties of light fields and discuss the concept
of squeezing and uncertainty relations for multimode light in the polarization
quantum optics. As a consequence, a new classification of polarization states
of quantum light is obtained. We also derive geometric phases acquired by
different quantum light beams transmitted through "polarization rotators".


title:
Relation between energy shifts and relaxation rates for a small system
  coupled to a reservoir

abstract:
  For a small system the coupling to a reservoir causes energy shifts as well
as transitions between the system's energy levels. We show for a general
stationary situation that the energy shifts can essentially be reduced to the
relaxation rates. The effects of reservoir fluctuations and self reaction are
treated separately. We apply the results to a two-level atom coupled to a
reservoir which may be the vacuum of a radiation field.


title: On the Global Existence of Bohmian Mechanics

abstract:
  We show that the particle motion in Bohmian mechanics, given by the solution
of an ordinary differential equation, exists globally: For a large class of
potentials the singularities of the velocity field and infinity will not be
reached in finite time for typical initial values. A substantial part of the
analysis is based on the probabilistic significance of the quantum flux. We
elucidate the connection between the conditions necessary for global existence
and the self-adjointness of the Schr\"odinger Hamiltonian.


title: Decoherence and the Quantum Zeno Effect

abstract:
  The experiment of Etano et al which demonstrated the quantum Zeno effect
(QZE) in an optical experiment was explained by Frerichs and Schenzle without
invoking the wave function collapse. In this report it is proposed that the
collapse does occur, and it can be explained by the `environment induced
decoherence' theory. The environment here consists of the completely quantized
field vacuum modes. The spontaneous emission life time of the atom sets a
fundamental limit on the requirement of `continuous measurements' for QZE. This
limit turns out to be related to the time-energy uncertainty relation discussed
by Ghirardi et al.


title: HyperDiamond Feynman Checkerboard in 4-dimensional Spacetime

abstract:
  A generalized Feynman Checkerboard model is constructed using a 4-dimensional
HyperDiamond lattice. The resulting phenomenological model is the D4-D5-E6
model described in hep-ph/9501252 and quant-ph/9503009.


title: Elementary gates for quantum computation

abstract:
  We show that a set of gates that consists of all one-bit quantum gates (U(2))
and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x
\oplus y)$) is universal in the sense that all unitary operations on
arbitrarily many bits $n$ (U($2^n$)) can be expressed as compositions of these
gates. We investigate the number of the above gates required to implement other
gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2)
transformation to one input bit if and only if the logical AND of all remaining
input bits is satisfied. These gates play a central role in many proposed
constructions of quantum computational networks. We derive upper and lower
bounds on the exact number of elementary gates required to build up a variety
of two-and three-bit quantum gates, the asymptotic number required for $n$-bit
Deutsch-Toffoli gates, and make some observations about the number required for
arbitrary $n$-bit unitary operations.


title: Conditional Quantum Dynamics and Logic Gates

abstract:
  Quantum logic gates provide fundamental examples of conditional quantum
dynamics. They could form the building blocks of general quantum information
processing systems which have recently been shown to have many interesting
non--classical properties. We describe a simple quantum logic gate, the quantum
controlled--NOT, and analyse some of its applications. We discuss two possible
physical realisations of the gate; one based on Ramsey atomic interferometry
and the other on the selective driving of optical resonances of two subsystems
undergoing a dipole--dipole interaction.


title:
ON THE QUANTUM EVOLUTION OF CHAOTIC SYSTEMS AFFECTED BY REPEATED
  FREQUENT MEASUREMENT

abstract:
  We investigate the effect of repeated measurement for quantum dynamics of the
suppressed systems which classical counterparts exhibit chaos. The essential
feature of such systems is the quantum localization phenomena strongly limiting
motion in the energy space. Repeated frequent measurement of suppressed systems
results to the delocalization. Time evolution of the observed chaotic systems
becomes close to the classical frequently broken diffusion-like process
described by rate equations for the probabilities rather than for amplitudes.


title: Gravity, energy conservation and parameter values in collapse models

abstract:
  We interpret the probability rule of the CSL collapse theory to mean that the
scalar field which causes collapse is the grvitational curvature scalar with
two sources, the expectation value of the mass density and a white noise
fluctuating source. We examine two models of the fluctuating source, monopole
fluctuations and dipole fluctuations, and show that these correspond to two
well known collapse models. We relate the two GRW parameters of CSL to
fundamental constants, and explain the energy increase as arising from the loss
of vacuum gravitational energy. It is shown how a problem with semi-classical
grvity may be cured when it is combined with a CSL collapse model.


title: Quantum Mechanics as a Classical Theory I: Non-relativistic Theory

abstract:
  The objective of this series of three papers is to axiomatically derive
quantum mechanics from classical mechanics and two other basic axioms. In this
first paper, Schreodinger's equation for the density matrix is fist obtained
and from it Schroedinger's equation for the wave functions is derived. The
momentum and position operators acting upon the density matrix are defined and
it is then demonstrated that they commute. Pauli's equation for the density
matrix is also obtained. A statistical potential formally identical to the
quantum potential of Bohm's hidden variable theory is introduced, and this
quantum potential is reinterpreted through the formalism here proposed. It is
shown that, for dispersion free {\it ensembles% }, Schroedinger's equation for
the density matrix is equivalent to Newton's equations. A general non-ambiguous
procedure for the construction of operators which act upon the density matrix
is presented. It is also shown how these operators can be reduced to those
which act upon the wave functions.


title: Quantum Mechanics as a Classical Theory II: Relativistic Theory

abstract:
  In this article, the axioms presented in the first one are reformulated
according to the special theory of relativity. Using these axioms, quantum
mechanic's relativistic equations are obtained in the presence of
electromagnetic fields for both the density function and the probability
amplitude. It is shown that, within the present theory's scope, Dirac's second
order equation should be considered the fundamental one in spite of the first
order equation. A relativistic expression is obtained for the statistical
potential. Axioms are again altered and made compatible with the general theory
of relativity. These postulates, together with the idea of the statistical
potential, allow us to obtain a general relativistic quantum theory for {\it
ensembles} composed of single particle systems.


title: Quantum Mechanics as a Classical Theory III: Epistemology

abstract:
  The two previous papers developed quantum mechanical formalism from classical
mechanics and two additional postulates. In the first paper it was also shown
that the uncertainty relations possess no ontological validity and only reflect
the formalism's limitations. In this paper, a Realist Interpretation of quantum
mechanics based on these results is elaborated and compared to the Copenhagen
Interpretation. We demonstrate that von Neumann's proof of the impossibility of
a hidden variable theory is not correct, independently of Bell's argumentation.
A local hidden variable theory is found for non-relativistic quantum mechanics,
which is nothing else than newtonian mechanics itself. We prove that Bell's
theorem does not imply in a non-locality of quantum mechanics, and also
demonstrate that Bohm's theory cannot be considered a true hidden variable
theory.


title: Quantum dynamics with two Planck constants and the semiclassical limit

abstract:
  The mathematical possibility of coupling two quantum dynamic systems having
two different Planck constants, respectively, is investigated. It turns out
that such canonical dynamics are always irreversible. Semiclassical dynamics is
obtained by letting one of the two Planck constants go to zero. This
semiclassical dynamics will preserve positivity, as expected, so an improvement
of the earlier proposals by Aleksandrov and by Boucher and Traschen is
achieved. Coupling of quantized matter to gravity is illustrated by a
simplistic example.


title: Quantum Mechanics as a Classical Theory IV: The Negative Mass Conjecture

abstract:
  The following two papers form a natural development of a previous series of
three articles on the foundations of quantum mechanics; they are intended to
take the theory there developed to its utmost logical and epistemological
consequences. We show in the first paper that relativistic quantum mechanics
might accommodate without ambiguities the notion of negative masses. To achieve
this, we rewrite all of its formalism for integer and half integer spin
particles and present the world revealed by this conjecture. We also base the
theory on the second order Klein-Gordon's and Dirac's equations and show that
they can be stated with only positive definite energies. In the second paper we
show that the general relativistic quantum mechanics derived in paper II of
this series supports this conjecture.


title:
Quantum Mechanics as a Classical Theory V: The Quantum Schwartzchild
  Problem

abstract:
  In this continuation paper, we apply the general relativistic quantum theory
for one particle systems, derived in paper II of this series, to a simple
problem: the quantum Schwartzchild problem, where one particle of mass {\it m%
} gravitates around a massive body. The results thus obtained reveal that, in
the realm of such a theory, the negative mass conjecture we made in paper IV of
this series is, indeed, adequate. It is shown that gravitation is responsible
for the loss of energy quantization. We relate this property with the ideas of
irreversibility and time arrow.


title: DYNAMICS OF SQUEEZING FROM GEMERALIZED COHERENT STATES

abstract:
  We extend the definition of generalized coherent states to include the case
of time-dependent dispersion. We introduce a suitable operator providing
displacement and dynamical rescaling from an arbitrary ground state. As a
consequence, squeezing is naturally embedded in this framework, and its
dynamics is ruled by the evolution equation for the dispersion. Our
construction provides a displacement-operator method to obtain the squeezed
states of arbitrary systems.


title:
Dissipative Quantum Systems with Potential Barrier. General Theory and
  Parabolic Barrier

abstract:
  We study the real time dynamics of a quantum system with potential barrier
coupled to a heat-bath environment. Employing the path integral approach an
evolution equation for the time dependent density matrix is derived. The time
evolution is evaluated explicitly near the barrier top in the temperature
region where quantum effects become important. It is shown that there exists a
quasi-stationary state with a constant flux across the potential barrier. This
state generalizes the Kramers flux solution of the classical Fokker-Planck
equation to the quantum regime. In the temperature range explored the quantum
flux state depends only on the parabolic approximation of the anharmonic
barrier potential near the top. The parameter range within which the solution
is valid is investigated in detail. In particular, by matching the flux state
onto the equilibrium state on one side of the barrier we gain a condition on
the minimal damping strength. For very high temperatures this condition reduces
to a known result from classical rate theory. Within the specified parameter
range the decay rate out of a metastable state is calculated from the flux
solution. The rate is shown to coincide with the result of purely thermodynamic
methods. The real time approach presented can be extended to lower temperatures
and smaller damping.


title: Quantum mechanics of time-dependent systems. Construction of pure states

abstract:
  For time-dependent systems the wavefunction depends explicitly on time and it
is not a pure state of the Hamiltonian. We construct operators for which the
above wavefunction is a pure state. The method is based on the introduction of
conserved quantities $Q$ and the pure states are defined by ${\hat
Q}\psi=q\psi$. The conserved quantities are constructed using parametrised
mechanics and the Noether theorem.


title: Quantum Cryptography

abstract:
  Quantum cryptography is a new method for secret communications offering the
ultimate security assurance of the inviolability of a Law of Nature. In this
paper we shall describe the theory of quantum cryptography, its potential
relevance and the development of a prototype system at Los Alamos, which
utilises the phenomenon of single-photon interference to perform quantum
cryptography over an optical fiber communications link.


title: Quantum Mechanical Coherence, Resonance, and Mind

abstract:
  Norbert Wiener and J.B.S. Haldane suggested during the early thirties that
the profound changes in our conception of matter entailed by quantum theory
opens the way for our thoughts, and other experiential or mind-like qualities,
to play a role in nature that is causally interactive and effective, rather
than purely epiphenomenal, as required by classical mechanics. The mathematical
basis of this suggestion is described here, and it is then shown how, by giving
mind this efficacious role in natural process, the classical character of our
perceptions of the quantum universe can be seen to be a consequence of
evolutionary pressures for the survival of the species.


title: Quantum Coding Theorem for Mixed States

abstract:
  We prove a theorem for coding mixed-state quantum signals. For a class of
coding schemes, the von Neumann entropy $S$ of the density operator describing
an ensemble of mixed quantum signal states is shown to be equal to the number
of spin-$1/2$ systems necessary to represent the signal faithfully. This
generalizes previous works on coding pure quantum signal states and is
analogous to the Shannon's noiseless coding theorem of classical information
theory. We also discuss an example of a more general class of coding schemes
which {\em beat} the limit set by our theorem.


title: Theory of Events

abstract:
  We review what we call "event-enhanced formalism" of quantum theory. In this
approach we explicitly assume classical nature of events. Given a quantum
system, that is coupled to a classical one by a suitable coupling, classical
events are being triggered. The trigerring process is partly random and partly
deterministic. Within this new approach one can modelize real experimental
events, including pointer readings of measuring devices. Our theory gives, for
the first time, a unique algorithm that can be used for computer generation of
experimental runs with individual quantum objects.


title: Higher order Schmidt decompositions

abstract:
  Necessary and sufficient conditions are given for the existence of extended
Schmidt decompositions, with more than two subspaces.


title: Rydberg Atoms Ionisation by Microwave Field and Electromagnetic Pulses

abstract:
  A simple theory of the Rydberg atoms ionisation by electromagnetic pulses and
microwave field is presented. The analysis is based on the scale transformation
which reduces the number of parameters and reveals the functional dependencies
of the processes. It is shown that the observed ionisation of Rydberg atoms by
subpicosecond electromagnetic pulses scale classically. The threshold electric
field required to ionise a Rydberg state may be simply evaluated in the
photonic basis approach for the quantum dynamics or from the multiphoton
ionisation theory.


title:
Photon states associated with Holstein-Primakoff realization of SU(1,1)
  Lie algebra

abstract:
  Statistical and phase properties and number-phase uncertainty relations are
systematically investigated for photon states associated with the
Holstein-Primakoff realization of the SU(1,1) Lie algebra. Perelomov's SU(1,1)
coherent states and the eigenstates of the SU(1,1) lowering generator (the
Barut-Girardello states) are discussed. A recently developed formalism, based
on the antinormal ordering of exponential phase operators, is used for studying
phase properties and number-phase uncertainty relations. This study shows
essential differences between properties of the Barut-Girardello states and the
SU(1,1) coherent states. The philophase states, defined as states with simple
phase-state representations, relate the quantum description of the optical
phase to the properties of the SU(1,1) Lie group. A modified Holstein-Primakoff
realization is derived, and eigenstates of the corresponding lowering generator
are discussed. These states are shown to contract, in a proper limit, to the
familiar Glauber coherent states.


title: Discrete photodetection and Susskind-Glogower ladder operators

abstract:
  We assert that state reduction processes in different types of photodetection
experiments are described by using different kinds of ladder operators. A
special model of discrete photodetection is developed by the use of
superoperators which are based on the Susskind-Glogower raising and lowering
operators.


title: A Survey on Bohmian Mechanics

abstract:
  Bohmian mechanics is the most naively obvious embedding imaginable of
Schr\"odinger's equation into a completely coherent physical theory. It
describes a world in which particles move in a highly non-Newtonian sort of
way, one which may at first appear to have little to do with the spectrum of
predictions of quantum mechanics. It turns out, however, that as a consequence
of the defining dynamical equations of Bohmian mechanics, when a system has
wave function $\psi$ its configuration is typically random, with probability
density $\rho$ given by $|\psi|^2$, the quantum equilibrium distribution. It
also turns out that the entire quantum formalism, operators as observables and
all the rest, is a consequence of Bohmian mechanics.


title:
The N-representability problem, the pseudo-spectral decomposition of
  antisymmetric 1-body operators, and collective behaviour

abstract:
  The pseudo--spectral decomposition of an $N$--particle antisymmetric 1--body
positive--semidefinite operator that corresponds to the canonical convex
decomposition into the extreme elements of the dual cone of the set of fermion
$N$--representable $1$--density operators has been derived. An attempt at
constucting a mathematical model for collective behaviour of a system of
$N$--fermions that originates from the pseudo--spectral decomposition is
presented.


title: LARGE ORDER ASYMPTOTICS OF SEMICLASSICAL EXPANSION: A NEW APPROACH

abstract:
  A new approach to the problem of finding the asymptotical behaviour of large
orders of semiclassical expansion is suggested. Asymptotics of high orders not
only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one
can apply not only functional integral technique, which has been used up to
now, but also method of direct analysis of the semiclassical expansion
recursive relations.


title: On the Lieb-Thirring constants L_gamma,1 for gamma geq 1/2

abstract:
  Let $E_i(H)$ denote the negative eigenvalues of the one-dimensional
Schr\"odinger operator $Hu:=-u^{\prime\prime}-Vu,\ V\geq 0,$ on $L_2({\Bbb
R})$. We prove the inequality \sum_i|E_i(H)|^\gamma\leq L_{\gamma,1}\int_{\Bbb
R} V^{\gamma+1/2}(x)dx, (1) for the "limit" case $\gamma=1/2.$ This will imply
improved estimates for the best constants $L_{\gamma,1}$ in (1), as
$1/2<\gamma<3/2.


title: ON THE LARGE ORDER ASYMPTOTICS OF THE WAVE FUNCTION PERTURBATION THEORY

abstract:
  The problem of finding the large order asymptotics for the eigenfunction
perturbation theory in quantum mechanics is studied. The relation between the
wave function argument x and the number of perturbation theory order k that
allows us to construct the asymptotics by saddle-point technique is found:
$x/k^{1/2}=const$, k is large. Classical euclidean solutions starting from the
classical vacuum play an important role in constructing such asymptotics. The
correspondence between the trajectory end and the parameter $x/k^{1/2}$ is
found. The obtained results can be applied to the calculation of the main
values of the observables depending on k in the k-th order of perturbation
theory at larges k and, probably, to the multiparticle production problem.


title: COMBINATORIAL COMPUTATION OF CLEBSCH-GORDAN COEFFICIENTS

abstract:
  The addition of angular momenta can be reduced to elementary coupling
processes of spin-$\frac{1}{2}$-particles. In this way, a method is developed
which allows for a non-recursive, simultaneous computation of all
Clebsch-Gordan coefficients concerning the addition of two angular momenta. The
relevant equations can be interpreted easily, analogously to simple
probabilistic considerations. They provide an improved understanding of the
addition of angular momenta as well as a practicable evaluation of
Clebsch-Gordan coefficients in an easier way than within the well-known
methods.


title: The classical limit of quantum theory

abstract:
  For a quantum observable $A_\hbar$ depending on a parameter $\hbar$ we define
the notion ``$A_\hbar$ converges in the classical limit''. The limit is a
function on phase space. Convergence is in norm in the sense that $A_\hbar\to0$
is equivalent with $\Vert A_\hbar\Vert\to0$. The $\hbar$-wise product of
convergent observables converges to the product of the limiting phase space
functions. $\hbar^{-1}$ times the commutator of suitable observables converges
to the Poisson bracket of the limits. For a large class of convergent
Hamiltonians the $\hbar$-wise action of the corresponding dynamics converges to
the classical Hamiltonian dynamics. The connections with earlier approaches,
based on the WKB method, or on Wigner distribution functions, or on the limits
of coherent states are reviewed.


title:
Supersymmetry of Demkov-Ostrovsky effective potentials in the R_0=0
  sector

abstract:
  We present a supersymmetric analysis of the wave problem with a
Demkov-Ostrovsky spherically symmetric class of focusing potentials at zero
energy. Following a suggestion of L\'evai, we work in the so-called R_0=0
sector in order to obtain the superpartner (fermionic) potentials within
Witten's supersymmetric procedure. General solutions of the superpotential for
the known physical cases are given explicitly.


title: Supersymmetric features of the Maxwell fish-eye lens

abstract:
  We provide a supersymmetric analysis of the Maxwell fisheye (MF) wave problem
at zero energy. Working in the so-called $R_{0}=0$ sector, we obtain the
corresponding superpartner (fermionic) MF effective potential within Witten's
one-dimensional (radial) supersymmetric procedure.


title: Unitary Evolution Between Pure and Mixed States

abstract:
  We propose an extended quantum mechanical formalism that is based on a wave
operator $\vr$, which is related to the ordinary density matrix via
$\rho=\vr\vr^\dagger$. This formalism allows a (generalized) unitary evolution
between pure and mixed states. It also preserves much of the connection between
symmetries and conservation laws. The new formalism is illustrated for the case
of a two level system.


title:
Experimental limit on the blue shift of the frequency of light implied
  by a q-nonlinearity

abstract:
  We discuss the implications of an experiment in which the frequencies of two
laser beams are compared for different intensities in order to search for a
dependence of the frequency of light on its intensity. Since no such dependence
was found it is possible to place bounds on a description of the
electromagnetic field in terms of q-oscillators. We conclude that the value of
the nonlinearity parameter is smaller than $10^{-17}~$.


title:
Quantization of electromagnetic field in inhomogeneous dispersive
  dielectrics

abstract:
  Canonical quantization of electromagnetic field inside the time--spatially
dispersive inhomogeneous dielectrics is presented. Interacting electromagnetic
and matter excitation fields create the closed system, Hamiltonian of which may
be diagonalized by generalized polariton transformation. Resulting dispersion
relations coincide with the classical ones obtained by the solution of wave
equation, the corresponding mode decomposition is, however, orthogonal and
complete in the enlarged Hilbert space.


title:
The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum
  Mechanics

abstract:
  The main purpose of the paper is an essentially probabilistic analysis of
relativistic quantum mechanics. It is based on the assumption that whenever
probability distributions arise, there exists a stochastic process that is
either responsible for temporal evolution of a given measure or preserves the
measure in the stationary case. Our departure point is the so-called
Schr\"{o}dinger problem of probabilistic evolution, which provides for a unique
Markov stochastic interpolation between any given pair of boundary probability
densities for a process covering a fixed, finite duration of time, provided we
have decided a priori what kind of primordial dynamical semigroup transition
mechanism is involved. In the nonrelativistic theory, including quantum
mechanics, Feyman-Kac-like kernels are the building blocks for suitable
transition probability densities of the process. In the standard "free" case
(Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered.
In the framework of the Schr\"{o}dinger problem, the "free noise" can also be
extended to any infinitely divisible probability law, as covered by the
L\'{e}vy-Khintchine formula. Since the relativistic Hamiltonians $|\nabla |$
and $\sqrt {-\triangle +m^2}-m$ are known to generate such laws, we focus on
them for the analysis of probabilistic phenomena, which are shown to be
associated with the relativistic wave (D'Alembert) and matter-wave
(Klein-Gordon) equations, respectively. We show that such stochastic processes
exist and are spatial jump processes. In general, in the presence of external
potentials, they do not share the Markov property, except for stationary
situations. A concrete example of the pseudodifferential Cauchy-Schr\"{o}dinger
evolution is analyzed in detail. The relativistic covariance of related wave


title:
The Rigged Hilbert Space Formulation of Quantum Mechanics and its
  Implications for Irreversibility

abstract:
  Quantum mechanics in the Rigged Hilbert Space formulation describes
quasistationary phenomena mathematically rigorously in terms of Gamow vectors.
We show that these vectors exhibit microphysical irreversibility, related to an
intrinsic quantum mechanical arrow of time, which states that preparation of a
state has to precede the registration of an observable in this state. Moreover,
the Rigged Hilbert Space formalism allows the derivation of an exact golden
rule describing the transition of a pure Gamow state into a mixture of
interaction-free decay products.


title:
A Selective Relaxation Method for Numerical Solution of Schr\"odinger
  Problems

abstract:
  We propose a numerical method for evaluating eigenvalues and eigenfunctions
of Schr\"odinger operators with general confining potentials. The method is
selective in the sense that only the eigenvalue closest to a chosen input
energy is found through an absolutely-stable relaxation algorithm which has
rate of convergence infinite. In the case of bistable potentials the method
allows one to evaluate the fundamental energy splitting for a wide range of
tunneling rates.

categories: quant-ph comp-gas cond-mat hep-lat nlin.CG


title: Second solution of Demkov-Ostrovsky superpotentials

abstract:
  We work out the second solution of the DO superpotentials in the $R_0=0$
sector.


title:
MARKOV DIFFUSIONS IN COMOVING COORDINATES AND STOCHASTIC QUANTIZATION OF
  THE FREE RELATIVISTIC SPINLESS PARTICLE

abstract:
  We revisit the classical approach of comoving coordinates in relativistic
hydrodynamics and we give a constructive proof for their global existence under
suitable conditions which is proper for stochastic quantization. We show that
it is possible to assign stochastic kinematics for the free relativistic
spinless particle as a Markov diffusion globally defined on ${\sf M}^4$. Then
introducing dynamics by means of a stochastic variational principle with
Einstein's action, we are lead to positive-energy solutions of Klein-Gordon
equation. The procedure exhibits relativistic covariance properties.


title: Review of R. Omnes, THE INTERPRETATION OF QUANTUM MECHANICS

abstract:
  Omnes' interpretation of quantum mechanics is summarized, and compared with
other consistent-history approaches by Gell-Mann and Hartle, and by Griffiths.


title: Consistent Quantum Reasoning

abstract:
  Precise rules are developed in order to formalize the reasoning processes
involved in standard non-relativistic quantum mechanics, with the help of
analogies from classical physics. A classical or quantum description of a
mechanical system involves a {\it framework}, often chosen implicitly, and a
{\it statement} or assertion about the system which is either true or false
within the framework with which it is associated. Quantum descriptions are no
less ``objective'' than their classical counterparts, but differ from the
latter in the following respects: (i) The framework employs a Hilbert space
rather than a classical phase space. (ii) The rules for constructing meaningful
statements require that the associated projectors commute with each other and,
in the case of time-dependent quantum histories, that consistency conditions be
satisfied. (iii) There are incompatible frameworks which cannot be combined,
either in constructing descriptions or in making logical inferences about them,
even though any one of these frameworks may be used separately for describing a
particular physical system.
  A new type of ``generalized history'' is introduced which extends previous
proposals by Omn\`es, and Gell-Mann and Hartle, and a corresponding consistency
condition which does not involve density matrices or single out a direction of
time. Applications which illustrate the formalism include: measurements of
spin, two-slit diffraction, and the emergence of the classical world from a
fully quantum description.


title: HIGH ORDER BEHAVIOUR OF PERTURBATION RECURSIVE RELATIONS

abstract:
  The problem of large order behaviour of perturbation theory for quantum
mechanical systems is considered. A new approach to it is developed. An
explicit mechanism showing the connection between large order recursive
relations and classical euclidean equations of motion is found. Large order
asymptotics of the solution to the recursive relations is constructed. The
developed method is applicable to the excited states, as well as to the ground
state. Singular points of the obtained asymptotics of the perturbation series
for eigenfunctions and density matrices are investigated and formulas being
valid near such points are obtained.


title: A Simple Quantum Computer

abstract:
  We propose an implementation of a quantum computer to solve Deutsch's
problem, which requires exponential time on a classical computer but only
linear time with quantum parallelism. By using a dual-rail qubit representation
as a simple form of error correction, our machine can tolerate some amount of
decoherence and still give the correct result with high probability. The design
which we employ also demonstrates a signature for quantum parallelism which
unambiguously delineates the desired quantum behavior from the merely
classical. The experimental demonstration of our proposal using quantum optical
components calls for the development of several key technologies common to
single photonics.


title:
Feynman-Kac Kernels in Markovian Representations of the Schroedinger
  Interpolating Dynamics

abstract:
  Probabilistic solutions of the so called Schr\"{o}dinger boundary data
problem provide for a unique Markovian interpolation between any two strictly
positive probability densities designed to form the input-output statistics
data for the process taking place in a finite-time interval. The key issue is
to select the jointly continuous in all variables positive Feynman-Kac kernel,
appropriate for the phenomenological (physical) situation. We extend the
existing formulations of the problem to cases when the kernel is \it not \rm a
fundamental solution of a parabolic equation, and prove the existence of a
continuous Markov interpolation in this case. Next, we analyze the
compatibility of this stochastic evolution with the original parabolic
dynamics, while assumed to be governed by the temporally adjoint pair of
(parabolic) partial differential equations, and prove that the pertinent random
motion is a diffusion process. In particular, in conjunction with Born's
statistical interpretation postulate in quantum theory, we consider stochastic
processes which are compatible with the Schr\"{o}dinger picture quantum
evolution.

categories: quant-ph adap-org chao-dyn chem-ph hep-th math.PR nlin.AO nlin.CD


title: Wavelet basis for the Schr\"{o}dinger equation

abstract: The self-similar representation for the Schr\"{o}dinger equation is derived.


title: [p,q] does not equal (i h-bar)

abstract:
  In this short note, I point out that [p,q] does not equal (i h-bar), contrary
to the original claims of Born and Jordan, and Dirac. Rather, [p,q] is equal to
something that is *infinitesimally different* from (i h-bar). While this
difference is usually harmless, it does provide the solution of the Born-Jordan
"trace paradox" of [p,q]. More recently, subtleties of a very similar form have
been found to be of fundamental importance in quantum field theory.


title: Quantum oblivious transfer protocols based on EPR states

abstract:
  We describe efficient protocols for quantum oblivious transfer and for
one-out-of-two quantum oblivious transfer. These protocols, which can be
implemented with present technology, are secure against general attacks as long
as the cheater can not store the bit for an arbitrarily long period of time.


title: A Universal Two--Bit Gate for Quantum Computation

abstract:
  We prove the existence of a class of two--input, two--output gates any one of
which is universal for quantum computation. This is done by explicitly
constructing the three--bit gate introduced by Deutsch [Proc.~R.~Soc.~London.~A
{\bf 425}, 73 (1989)] as a network consisting of replicas of a single two--bit
gate.


title: Realism and Time Symmetry in Quantum Mechanics

abstract:
  We describe a gedanken experiment with an interferometer in the case of pre-
and postselection in two different time symmetric ways: We apply the ABL
formalism and the de Broglie--Bohm model. Interpreting these descriptions
ontologically, we get two very different concepts of reality. Finally, we
discuss some problems implied by these concepts.


title: Universality in Quantum Computation

abstract:
  We show that in quantum computation almost every gate that operates on two or
more bits is a universal gate. We discuss various physical considerations
bearing on the proper definition of universality for computational components
such as logic gates.


title: A Quantum Bit Commitment Protocol Based on EPR States

abstract:
  A protocol for quantum bit commitment is proposed. The protocol is feasible
with present technology and is secure against cheaters with unlimited computing
power as long as the sender does not have the technology to store an EPR
particle for an arbitrarily long period of time. The protocol is very
efficient, requiring only tens of particles.


title: Randomness, Nonlocality and information in entagled correlations

abstract:
  It is shown that the Einstein, Podolsky and Rosen (EPR) correlations for
arbitrary spin-s and the Greenberger, Horne and Zeilinger (GHZ) correlations
for three particles can be described by nonlocal joint and conditional quantum
probabilities. The nonlocality of these probabilities makes the Bell's
inequalities void. A description that exhibits the relation between the
randomness and the nonlocality of entangled correlations is introduced.
Entangled EPR and GHZ correlations are studied using the Gibbs-Shannon entropy.
The nonlocal character of the EPR correlations is tested using the information
Bell's inequalities. Relations between the randomness, the nonlocality and the
entropic information for the EPR and the GHZ correlations are established and
discussed.


title: Spin-Orbit Pendulum: the Microscopic Stern-Gerlach Effect

abstract:
  The motion of a particle with a spin in spherical harmonic oscillator
potential with spin-orbit interaction is studied. We have focus our attention
on spatial motion of wave packets, giving a description complementary to motion
of spin discussed already in [1]. The particular initial conditions studied
here lead to the most transparent formulas and can be treated analytically. A
strong analogy with the Stern-Gerlach experiment is suggested. [1] R.Arvieu and
P.Rozmej, Phys.Rev.A50 (1994) 4376.


title: Nonlinear Schroedinger Dynamics and Nonlinear Observables

abstract:
  It is is explained why physical consistency requires substituting linear
observables by nonlinear ones for quantum systems with nonlinear time evolution
of pure states. The exact meaning and the concrete physical interpretation are
described in full detail for a special case of the nonlinear Doebner-Goldin
equation.


title: The Hard Problem: A Quantum Approach

abstract:
  Contents:
  1. Introduction: Philosophical Setting
  2. Quantum Model of the Mind/Brain
  3. Person and Self
  4. Meeting Baars's Criteria for Consciousness
  5. Qualia
  6. Free-Will


title: Geometry of One-Dimensional Wave Propagation

abstract:
  We investigate the geometrical features of one-dimensional wave propagation,
whose dynamics is described by the (2+1)-dimensional Lorentz group. We find
many interesting geometrical ingredients such as spinorlike behavior of wave
amplitudes, gauge transformations, Bloch-type equations, and Lorentz-group
Berry phases. We also propose an optical experiment to verify these effects.


title: A Local Deterministic Model of Quantum Spin Measurement

abstract:
  The conventional view, that Einstein was wrong to believe that quantum
physics is local and deterministic, is challenged. A parametrised model, Q, for
the state vector evolution of spin 1/2 particles during measurement is
developed. Q draws on recent work on so-called riddled basins in dynamical
systems theory, and is local, deterministic, nonlinear and time asymmetric.
Moreover the evolution of the state vector to one of two chaotic attractors
(taken to represent observed spin states) is effectively uncomputable.
Motivation for this model arises from Penrose's speculations about the nature
and role of quantum gravity. Although the evolution of Q's state vector is
uncomputable, the probability that the system will evolve to one of the two
attractors is computable. These probabilities correspond quantitatively to the
statistics of spin 1/2 particles. In an ensemble sense the evolution of the
state vector towards an attractor can be described by a diffusive random walk.
Bell's theorem and a version of the Bell-Kochen_specker quantum entanglement
paradox are discussed. It is shown that proving an inconsistency with locality
demands the existence of definite truth values to certain counterfactual
propositions. In Q these deterministic propositions are physically uncomputable
and no non-algorithmic solution is either known or suspected. Adapting the
mathematical formalist approach, the non-existence of definite truth values to
such counterfactual propositions is posited. No inconsistency with experiment
is found. Hence Q is not necessarily constrained by Bell's inequality.


title: Entropy of phase measurement: Quantum phase via quadrature measurement

abstract:
  The content of phase information of an arbitrary phase--sensitive measurement
is evaluated using the maximum likelihood estimation. The phase distribution is
characterized by the relative entropy--a nonlinear functional of input quantum
state. As an explicit example the multiple measurement of quadrature operator
is interpreted as quantum phase detection achieving the ultimate resolution
predicted by the Fisher information.


title: A NOTE ON DEGENERATE AND ANAMOLOUS BOSONS

abstract:
  In this note it is shown that for a mono-energetic collection of Bosons, at a
certain (non-zero) momentum or temperature, there is condensation while there
is another momentum or temperature at which there is infinite dilution and
below which the gas exhibits anomalous Fermionic behaviour.


title:
Precise Determination of the Energy Levels of the Anharmonic Oscillator
  from the Quantization of the Angle Variable

abstract:
  Using an ansatz motivated by the classical form of $e^{i\phi}$, where $\phi$
is the angle variable, we construct operators which satisfy the commutation
relations of the creation-annihilation operators for the anharmonic oscillator.
The matrix elements of these operators can be expressed in terms of {\it
entire} functions in the position complex plane. These functions provide
solutions of the Ricatti equation associated with the time-independent
Schr\"odinger equation. We relate the normalizability of the eigenstates to the
global properties of the flows of this equation. These exact results yield
approximations which complement the WKB approximation and allow an arbitrarily
precise determination of the energy levels. We give numerical results for the
first 10 levels with 30 digits. We address the question of the quantum
integrability of the system.


title: All local quantum states are mixtures of direct products

abstract:
  According to Popescu's recent analysis [Phys. Rev. Lett. {\bf72}, 797
(1994)], {\it nonideal} measurements, rather than ideal ones, may be more
sensitive to reveal nonlocal correlations between distant parts of composite
quantum systems. The outcome statistics of joint nonideal measurements on local
states should by definition admit local hidden variable models. We prove that
the density operator of a local composite system must be convex mixture of the
subsystems' density operators. This result depends essentially on a plausible
consistency condition restricting the class of admissible local hidden variable
models.


title: Mechanical Effects of Radiation Pressure Quantum Fluctuations

abstract:
  As revealed by space-time probing, mechanics and field theory come out as
complementary descriptions for motions in space-time. In particular, quantum
fields exert a radiation pressure on scatterers which results in mechanical
effects that persist in vacuum. They include mean forces due to quantum field
fluctuations, like Casimir forces, but also fluctuations of these forces and
additional forces linked to motion. As in classical electron theory, a moving
scatterer is submitted to a radiation reaction force which modifies its
motional response to an applied force. We briefly survey the mechanical effects
of quantum field fluctuations and discuss the consequences for stability of
motion in vacuum and for position fluctuations.


title: Quantum Fluctuations and Inertia

abstract:
  Vacuum field fluctuations exert a radiation pressure which induces mechanical
effects on scatterers. The question naturally arises whether the energy of
vacuum fluctuations gives rise to inertia and gravitation in agreement with the
general principles of mechanics. As a new approach to this question, we discuss
the mechanical effects of quantum field fluctuations on two mirrors building a
Fabry-Perot cavity. We first put into evidence that the energy related to
Casimir forces is an energy stored on field fluctuations as a result of
scattering time delays. We then discuss the forces felt by the mirrors when
they move within vacuum field fluctuations, and show that energy stored on
vacuum fluctuations contributes to inertia in conformity with the law of
inertia of energy. As a further consequence, inertial masses exhibit quantum
fluctuations with characteristic spectra in vacuum.


title: Quantum Limits in Space-Time Measurements

abstract:
  Quantum fluctuations impose fundamental limits on measurement and space-time
probing. Although using optimised probe fields can allow to push sensitivity in
a position measurement beyond the "standard quantum limit", quantum
fluctuations of the probe field still result in limitations which are
determined by irreducible dissipation mechanisms. Fluctuation-dissipation
relations in vacuum characterise the mechanical effects of radiation pressure
vacuum fluctuations, which lead to an ultimate quantum noise for positions. For
macroscopic reflectors, the quantum noise on positions is dominated by
gravitational vacuum fluctuations, and takes a universal form deduced from
quantum fluctuations of space-time curvatures in vacuum. These can be
considered as ultimate space-time fluctuations, fixing ultimate quantum limits
in space-time measurements.


title:
ARBITRARY-ORDER HERMITE GENERATING FUNCTIONS FOR COHERENT AND SQUEEZED
  STATES

abstract:
  For use in calculating higher-order coherent- and squeezed- state quantities,
we derive generalized generating functions for the Hermite polynomials. They
are given by $\sum_{n=0}^{\infty}z^{jn+k}H_{jn+k}(x)/(jn+k)!$, for arbitrary
integers $j\geq 1$ and $k\geq 0$. Along the way, the sums with the Hermite
polynomials replaced by unity are also obtained. We also evaluate the action of
the operators $\exp[a^j(d/dx)^j]$ on well-behaved functions and apply them to
obtain other sums.


title:
Long-Term Evolution and Revival Structure of Rydberg Wave Packets for
  Hydrogen and Alkali-Metal Atoms

abstract:
  This paper begins with an examination of the revival structure and long-term
evolution of Rydberg wave packets for hydrogen. We show that after the initial
cycle of collapse and fractional/full revivals, which occurs on the time scale
$t_{\rm rev}$, a new sequence of revivals begins. We find that the structure of
the new revivals is different from that of the fractional revivals. The new
revivals are characterized by periodicities in the motion of the wave packet
with periods that are fractions of the revival time scale $t_{\rm rev}$. These
long-term periodicities result in the autocorrelation function at times greater
than $t_{\rm rev}$ having a self-similar resemblance to its structure for times
less than $t_{\rm rev}$. The new sequence of revivals culminates with the
formation of a single wave packet that more closely resembles the initial wave
packet than does the full revival at time $t_{\rm rev}$, i.e., a superrevival
forms. Explicit examples of the superrevival structure for both circular and
radial wave packets are given. We then study wave packets in alkali-metal
atoms, which are typically used in experiments. The behavior of these packets
is affected by the presence of quantum defects that modify the hydrogenic
revival time scales and periodicities. Their behavior can be treated
analytically using supersymmetry-based quantum-defect theory. We illustrate our
results for alkali-metal atoms with explicit examples of the revival structure
for radial wave packets in rubidium.


title: Sensible Quantum Mechanics: Are Only Perceptions Probabilistic?

abstract:
  Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so
that it contains nothing probabilistic, except, in a certain frequency sense,
conscious perceptions. Sets of these perceptions can be deterministically
realized with measures given by expectation values of positive-operator-valued
awareness operators in a quantum state of the universe which never jumps or
collapses. Ratios of the measures for these sets of perceptions can be
interpreted as frequency-type probabilities for many actually existing sets
rather than as propensities for potentialities to be actualized, so there is
nothing indeterministic in SQM. These frequency-type probabilities generally
cannot be given by the ordinary quantum "probabilities" for a single set of
alternatives. Probabilism, or ascribing probabilities to unconscious aspects of
the world, may be seen to be an aesthemamorphic myth.
  No fundamental correlation or equivalence is postulated between different
perceptions (each being the entirety of a single conscious experience and thus
not in direct contact with any other), so SQM, a variant of Everett's
"many-worlds" framework, is a "many-perceptions" framework but not a
"many-minds" framework. Different detailed SQM theories may be tested against
experienced perceptions by the typicalities (defined herein) they predict for
these perceptions. One may adopt the Conditional Aesthemic Principle: among the
set of all conscious perceptions, our perceptions are likely to be typical.
  An experimental test is proposed to compare SQM with a variant, SQMn.


title: Computation of Structure Functions From a Lattice Hamiltonian

abstract:
  We suggest to compute structure functions in the Hamiltonian formalism on a
momentum lattice using a physically motivated regularisation that links the
total parton number to the lattice size. We show for the $\phi ^4 _4$ theory
that our method allows to describe continuum physics. The critical line and the
renormalised mass spectrum close to that critical line are computed and scaling
behaviour is observed in good agreement with the semi-analytical results of
L{\"u}scher and Weisz and with other lattice simulations. We also demonstrate
that our method is able to reproduce the $Q^2$ behaviour of deep inelastic
structure functions and the typical peak at $x_B=0.$


title: One-way Functions In Reversible Computations

abstract:
  One-way functions are used in modern cryto-systems as doortraps because their
inverse functions are supposed to be difficult to compute. Nonetheless with the
discovery of reversible computation, it seems that one may break a one-way
function by running a reversible computer backward. Here, we argue that
reversible computation alone poses no threat to the existence of one-way
functions because of the generation of ``garbage bits'' during computations.
Consequently, we prove a necessary and sufficient condition for a one-to-one
function to be a one-way in terms of the growth rate of the total number of
possible garbage bit configurations with the input size.


title: Quantum Fields a la Sylvester and Witt

abstract:
  A structural explanation of the coupling constants in the standard model, i.e
the fine structure constant and the Weinberg angle, and of the gauge fixing
contributions is given in terms of symmetries and representation theory. The
coupling constants are normalizations of Lorentz invariantly embedded little
groups (spin and polarization) arising in a harmonic analysis of quantum vector
fields. It is shown that the harmonic analysis of massless fields requires an
extension of the familiar Fourier decomposition, containing also indefinite
unitary nondecomposable time representations. This is illustrated by the
nonprobabilistic contributions in the electromagnetic field.


title: Quantum Mechanics with Event Dynamics

abstract:
  Event generating algorithm corresponding to a linear master equation of
Lindblad's type is described and illustrated on two examples: that of a
particle detector and of a fuzzy clock. Relation to other approaches to
foundations of quantum theory and to description of quantum measurements is
briefly discussed.


title: On Wolter's vortex in total reflection

abstract:
  The "circulatory wave" ("die zirkulierende Welle") put into evidence in 1949
by Wolter (Wolter's vortex) in total reflection is interpreted as a phase
defect in the scalar theory of Green and Wolf of 1953, which is the Madelung
(hydrodynamic) representation of the optical field. Some comments are added on
its possible relevance for the Hamamatsu experiment aimed to clarify the
wave-particle duality at the "single photon" level of down-converted laser
beams


title:
Using Classical Probability To Guarantee Properties of Infinite Quantum
  Sequences

abstract:
  We consider the product of infinitely many copies of a spin-$1\over 2$
system. We construct projection operators on the corresponding nonseparable
Hilbert space which measure whether the outcome of an infinite sequence of
$\sigma^x$ measurements has any specified property. In many cases, product
states are eigenstates of the projections, and therefore the result of
measuring the property is determined. Thus we obtain a nonprobabilistic quantum
analogue to the law of large numbers, the randomness property, and all other
familiar almost-sure theorems of classical probability.


title:
Events and Piecewise Deterministic Dynamics in Event-Enhanced Quantum
  Theory

abstract:
  We enhance the standard formalism of quantum theory to enable events. The
concepts of experiment and of measurement are defined. Dynamics is given by
Liouville's equation that couples quantum system to a classical one. It implies
a unique Markov process involving quantum jumps, classical events and
describing sample histories of individual systems.


title: Interaction-Free Preparation

abstract:
  We demonstrate that the preparation of a very well localized atom beam is
possible without physical interaction. The preparation is based on the
selection of an adequate ensemble of atoms of an originally wide beam by means
of information obtained with a neutron interferometer. In such a case the
uncertainty relation can no longer be interpreted as a by-product of the
interaction between the system and the preparation apparatus.


title:
The Emergence of Classicality via Decoherence Described by Lindblad
  Operators

abstract:
  Zurek, Habib and Paz [W. H. Zurek, S. Habib and J. P. Paz, Phys. Rev. Lett.
{\bf 70} (1993)\ 1187] have characterized the set of states of maximal
stability defined as the set of states having minimum entropy increase due to
interaction with an environment, and shown that coherent states are maximal for
the particular environment model examined. To generalize these results, I
consider entropy production within the Lindblad theory of open systems,
treating environment effects perturbatively. I characterize the maximally
predicitive states which emerge from several forms of effective dynamics,
including decoherence from spatially correlated noise. Under a variety of
conditions, coherent states emerge as the maximal states.


title: Decoherence: Basic Concepts and Their Interpretation

abstract:
  Introduction to the theory of decoherence. Contents: 1. The phenomenon of
decoherence: superpositions, superselection rules, decoherence by
"measurements". 2. Observables as a derivable concept. 3. The measurement
problem. 4. Density matrix, coarse graining, and "events". 5. Conclusions.


title: An Operator Derivation of the Path Decomposition Expansion

abstract:
  The path decomposition expansion is a path integral technique for decomposing
sums over paths in configuration space into sums over paths in different
spatial regions. It leads to a decomposition of the configuration space
propagator across arbitrary surfaces in configuration space. It may be used,
for example, in calculations of the distribution of first crossing times. The
original proof relied heavily on the position representation and in particular
on the properties of path integrals. In this paper, an elementary proof of the
path decomposition expansion is given using projection operators. This leads to
a version of the path decomposition expansion more general than the
configuration space form previously given. The path decomposition expansion in
momentum space is given as an example.


title:
Relativistic nuclear recoil corrections to the energy levels of
  hydrogen-like and high $Z$ lithium like atoms in all orders in $\alpha Z$

abstract:
  The relativistic nuclear recoil corrections to the energy levels of
low-laying states of hydrogen-like and high $Z$ lithium-like atoms in all
orders in $\alpha Z$ are calculated. The calculations are carried out using the
B-spline method for the Dirac equation.
  For low $Z$ the results of the calculation are in good agreement with the
$\alpha Z$ -expansion results. It is found that the nuclear recoil
contribution, additional to the Salpeter's one, to the Lamb shift ($n=2$) of
hydrogen is $-1.32(6)\,kHz$. The total nuclear recoil correction to the energy
of the $(1s)^{2}2p_{\frac{1}{2}}-(1s)^{2}2s$ transition in lithium-like uranium
constitutes $-0.07\,eV$ and is largely made up of QED contributions.


title: Sonoluminescence as quantum vacuum radiation

abstract:
  Sonoluminescence is explained in terms of quantum radiation by moving
interfaces between media of different polarizability. It can be considered as a
dynamic Casimir effect, in the sense that it is a consequence of the imbalance
of the zero-point fluctuations of the electromagnetic field during the
non-inertial motion of a boundary. The transition amplitude from the vacuum
into a two-photon state is calculated in a Hamiltonian formalism and turns out
to be governed by the transition matrix-element of the radiation pressure.
Expressions for the spectral density and the total radiated energy are given.


title: Theory of quantum radiation observed as sonoluminescence

abstract:
  Sonoluminescence is explained in terms of quantum radiation by moving
interfaces between media of different polarizability. In a stationary
dielectric the zero-point fluctuations of the electromagnetic field excite
virtual two-photon states which become real under perturbation due to motion of
the dielectric. The sonoluminescent bubble is modelled as an optically empty
cavity in a homogeneous dielectric. The problem of the photon emission by a
cavity of time-dependent radius is handled in a Hamiltonian formalism which is
dealt with perturbatively up to first order in the velocity of the bubble
surface over the speed of light. A parameter-dependence of the zero-order
Hamiltonian in addition to the first-order perturbation calls for a new
perturbative method combining standard perturbation theory with an adiabatic
approximation. In this way the transition amplitude from the vacuum into a
two-photon state is obtained, and expressions for the single-photon spectrum
and the total energy radiated during one flash are given both in full and in
the short-wavelengths approximation when the bubble is larger than the
wavelengths of the emitted light. It is shown analytically that the spectral
density has the same frequency-dependence as black-body radiation; this is
purely an effect of correlated quantum fluctuations at zero temperature. The
present theory clarifies a number of hitherto unsolved problems and suggests
explanations for several more. Possible experiments that discriminate this from
other theories of sonoluminescence are proposed.


title: Holstein-Primakoff/Bogoliubov Transformations and the Multiboson System

abstract:
  As an aid to understanding the {\it displacement operator} definition of
squeezed states for arbitrary systems, we investigate the properties of systems
where there is a Holstein-Primakoff or Bogoliubov transformation. In these
cases the {\it ladder-operator or minimum-uncertainty} definitions of squeezed
states are equivalent to an extent displacement-operator definition. We
exemplify this in a setting where there are operators satisfying $[A,
A^{\dagger}] = 1$, but the $A$'s are not necessarily the Fock space $a$'s; the
multiboson system. It has been previously observed that the ground state of a
system often can be shown to to be a coherent state. We demonstrate why this
must be so. We close with a discussion of an alternative, effective definition
of displacement-operator squeezed states.


title: Quantum Mechanics, Chaos and the Bohm Theory

abstract:
  The quantum counterpart of the classically chaotic kicked rotor is
investigated using Bohm's appraoch to quantum theory.


title: Measurement, Decoherence and Chaos in Quantum Pinball

abstract:
  The effect of introducing measuring devices in a ``quantum pinball'' system
is shown to lead to a chaotic evolution for the particle position as defined in
Bohm's approach to Quantum Mechanics.


title: Quantum logic and decohering histories

abstract:
  An introduction is given to an algebraic formulation and generalisation of
the consistent histories approach to quantum theory. The main technical tool in
this theory is an orthoalgebra of history propositions that serves as a
generalised temporal analogue of the lattice of propositions of standard
quantum logic. Particular emphasis is placed on those cases in which the
history propositions can be represented by projection operators in a Hilbert
space, and on the associated concept of a `history group'.


title: Decoherence and the Quantum Zeno Effect

abstract:
  The measurements in the optical test of quantum Zeno effect [Itano et al.
Phys. Rev. A\underbar{41} (1990) 2295) are analyzed using the
environment-induced decoherence theory, where the spontaneous emission lifetime
of the relevant level emerges as the 'decoherence time'. The implication of
this finite decoherence time in setting a fundamental limit on the
realizability of the condition of continuous measurements is investigated in
detail.


title: Applications of a Simple Formula

abstract:
  New applications of the formula $A |\psi\rangle = \langle A \rangle
|\psi\rangle + \Delta A |\psi_{\perp} \rangle$ are discussed. Simple
derivations of the Heisenberg uncertainty principle and of related inequalities
are presented. In addition, the formula is used in an instructive paradox which
clarifies a fundamental notion in quantum mechanics.


title: Decoherence and classical predictability of phase space histories

abstract:
  We consider the decoherence of phase space histories in a class of quantum
Brownian motion models, consisting of a particle moving in a potential $V(x)$
in interaction with a heat bath at temperature $T$ and dissipation gamma, in
the Markovian regime. The evolution of the density operator for this open
system is thus described by a non-unitary master equation. The phase space
histories of the system are described by a class of quasiprojectors.
Generalizing earlier results of Hagedorn and Omn\`es, we show that a phase
space projector onto a phase space cell $\Gamma$ is approximately evolved under
the master equation into another phase space projector onto the classical
dissipative evolution of $\Gamma$, and with a certain amount of degradation due
to the noise produced by the environment. We thus show that histories of phase
space samplings approximately decohere, and that the probabilities for these
histories are peaked about classical dissipative evolution, with a width of
peaking depending on the size of the noise.


title: Weak Decoherence and Quantum Trajectory Graphs

abstract:
  Griffiths' ``quantum trajectories'' formalism is extended to describe weak
decoherence. The decoherence conditions are shown to severely limit the
complexity of histories composed of fine-grained events.


title:
Nonlinear Gauge Transformations and Exact Solutions of the
  Doebner-Goldin Equation

abstract:
  Invariants of nonlinear gauge transformations of a family of nonlinear
Schr\"odinger equations proposed by Doebner and Goldin are used to characterize
the behaviour of exact solutions of these equations.


title: Approximate and Exact Consistency of Histories

abstract:
  The consistent histories formalism is discussed using path-projected states.
These are used to analyse various criteria for approximate consistency. The
connection between the Dowker-Halliwell criterion and sphere packing problems
is shown and used to prove several new bounds on the violation of probability
sum rules. The quantum Zeno effect is also analysed within the consistent
histories formalism and used to demonstrate some of the difficulties involved
in discussing approximate consistency. The complications associated with null
histories and infinite sets are briefly discussed.


title: Values and the Quantum Conception of Man

abstract:
  Classical mechanics is based upon a mechanical picture of nature that is
fundamentally incorrect. It has been replaced at the basic level by a radically
different theory: quantum mechanics. This change entails an enormous shift in
our basic conception of nature, one that can profoundly alter the scientific
image of man himself. Self-image is the foundation of values, and the
replacement of the mechanistic self-image derived from classical mechanics by
one concordant with quantum mechanics may provide the foundation of a moral
order better suited to our times, a self-image that endows human life with
meaning, responsibility, and a deeper linkage to nature as a whole.


title: Atom in a $q$-Analog Harmonic Oscillator Trap

abstract:
  We study the population inversion and Q-function of a two-level atom,
interacting with single-mode laser light field, in a $q$-analog harmonic
oscillator trap for increasing $q$. For $\tau=.003(q=e^{\tau})$ the collapses
and revivals of population inversion become well defined facilitating
experimental observation but for large $\tau \sim 0.1$ the time dependence of
population inversion is completely wiped out.


title:
Symmetry, Local Linearization, and Gauge Classification of the
  Doebner-Goldin Equation

abstract:
  For the family of nonlinear Schr\"odinger equations derived by H.-D.~Doebner
and G.A.~Goldin (J.Phys.A 27, 1771) we calculate the complete set of Lie
symmetries. For various subfamilies we find different finite and infinite
dimensional Lie symmetry algebras. Two of the latter lead to a local
transformation linearizing the particular subfamily. One type of these
transformations leaves the whole family of equations invariant, giving rise to
a gauge classification of the family. The Lie symmetry algebras and their
corresponding subalgebras are finally characterized by gauge invariant
parameters.


title: Potential Effect: Aharonov-Bohm Effect of Simply Connected Region

abstract:
  We study a generalization of Aharonov-Bohm effect, the potential effect. The
discussion is focused on field-free effects in simply connected region, which
obviously can not have any local field-flux. Among the published discussions
about this kind of effects, it is generally agreed that this kind of effects
does not exist due to gauge invariance. However, there are also opinions that
this effect is a trivial variation of Aharonov-Bohm effect and therefore there
is no need to check its existence. To my knowledge, it has never been tested.
My first goal here is to supply enough theoretical reason to motivate the
experimental test of this effect. I start with an intuitive derivation, then I
introduce a wave-front theory as a theoretical consideration. Logically, the
existence of potential effect implies the existence of the AB effect, but not
vice versa. The purpose of this paper is to provide a physical connection in
the opposite direction.


title: Quantum state diffusion, localization and computation

abstract:
  Numerical simulation of individual open quantum systems has proven advantages
over density operator computations. Quantum state diffusion with a moving basis
(MQSD) provides a practical numerical simulation method which takes full
advantage of the localization of quantum states into wave packets occupying
small regions of classical phase space. Following and extending the original
proposal of Percival, Alber and Steimle, we show that MQSD can provide a
further gain over ordinary QSD and other quantum trajectory methods of many
orders of magnitude in computational space and time. Because of these gains, it
is even possible to calculate an open quantum system trajectory when the
corresponding isolated system is intractable. MQSD is particularly advantageous
where classical or semiclassical dynamics provides an adequate qualitative
picture but is numerically inaccurate because of significant quantum effects.
The principles are illustrated by computations for the quantum Duffing
oscillator and for second harmonic generation in quantum optics. Potential
applications in atomic and molecular dynamics, quantum circuits and quantum
computation are suggested.