title: Does Quantum Mechanics Save Free Will?

abstract:
  According to the widely accepted opinion, classical (statistical) physics
does not support objective indeterminism, since the statistical laws of
classical physics allow a deterministic hidden background, while --- as Arthur
Fine writes polemizing with Gr\"unbaum --- "{\sl the antilibertarian position
finds little room to breathe in a statistical world if we take laws of the
quantum theory as exemplars of the statistical laws in such a world. So, it
appears that, contrary to what Gr\"unbaum claims, the libertarians' 'could have
done otherwise' does indeed find support from indeterminism if we take the
indeterministic laws to be of the sort found in the quantum theory.}" In this
paper I will show that, quite the contrary, quantum mechanics does not save
free will. For instance, the EPR experiments are compatible with a
deterministic world. They admit a deterministic local hidden parameter
description if the deterministic model is 'allowed' to describe not only the
measurement outcomes, but also the outcomes of the 'decisions' whether this or
that measurement will be performed. So, the derivation of the freedom of the
will from quantum mechanics is a tautology: from the assumption that the world
is indeterministic it is derived that the world cannot be deterministic.


title: Logic programming as quantum measurement

abstract:
  The emphasis is made on the juxtaposition of (quantum~theorem) proving versus
quantum (theorem~proving). The logical contents of verification of the
statements concerning quantum systems is outlined. The Zittereingang (trembling
input) principle is introduced to enhance the resolution of predicate
satisfiability problem provided the processor is in a position to perform
operations with continuous input. A realization of Zittereingang machine by a
quantum system is suggested.


title: Why we don't see the Schr\"odinger's cat state?

abstract:
  Schr\"odinger's cat puzzle is resolved. The reason why we do not see a
macroscopic superposition of states is cleared in the light of Everett's
formulation of quantum mechanics.


title: Newtonian Quantum Gravity

abstract:
  Puts forward a complete scenario for interpreting nonlinear field theories
highlighting the role played by gravitational self--energy in enabling a
consistent revival of the Schroedinger approach to unifying micro and macro
physics.


title:
Nonnegative Feynman-Kac Kernels in Schr\"{o}dinger's Interpolation
  Problem

abstract:
  The existing formulations of the Schr\"{o}dinger interpolating dynamics,
which is constrained by the prescribed input-output statistics data, utilize
strictly positive Feynman-Kac kernels. This implies that the related Markov
diffusion processes admit vanishing probability densities only at the
boundaries of the spatial volume confining the process. We extend the framework
to encompass singular potentials and associated nonnegative Feynman-Kac-type
kernels. It allows to deal with general nonnegative solutions of the
Schr\"{o}dinger boundary data problem. The resulting stochastic processes are
capable of both developing and destroying nodes (zeros) of probability
densities in the course of their evolution.


title: The unitary transformation of the path-integral measure

abstract:
  The aim of the article is to show how a coordinate transformation can be
applied to the path-integral formalism. For this purpose the unitary definition
of the quantum measure, which guarantees the conservation of total probability,
is offered. As the examples, the phase space transformation to the canonically
conjugate pare $(energy, time)$ and the transformation to the cylindrical
coordinates are shown. The transformations of the path-integral measure looks
classically but they can not be deduced from naive transformations of quantum
trajectories.


title:
Generalized uncertainty relations: Theory, examples, and Lorentz
  invariance

abstract:
  The quantum-mechanical framework in which observables are associated with
Hermitian operators is too narrow to discuss measurements of such important
physical quantities as elapsed time or harmonic-oscillator phase. We introduce
a broader framework that allows us to derive quantum-mechanical limits on the
precision to which a parameter---e.g., elapsed time---may be determined via
arbitrary data analysis of arbitrary measurements on $N$ identically prepared
quantum systems. The limits are expressed as generalized Mandelstam-Tamm
uncertainty relations, which involve the operator that generates displacements
of the parameter---e.g., the Hamiltonian operator in the case of elapsed time.
This approach avoids entirely the problem of associating a Hermitian operator
with the parameter. We illustrate the general formalism, first, with
nonrelativistic uncertainty relations for spatial displacement and momentum,
harmonic-oscillator phase and number of quanta, and time and energy and,
second, with Lorentz-invariant uncertainty relations involving the displacement
and Lorentz-rotation parameters of the Poincar\'e group.


title:
Variational Interpolation Algorithm between Weak- and Strong-Coupling
  Expansions

abstract:
  For many physical quantities, theory supplies weak- and strong-coupling
expansions of the types $\sum a_n \alpha ^n$ and $ \alpha ^p\sum b_n
(\alpha^{-2/q) ^n$, respectively. Either or both of these may have a zero
radius of convergence. We present a simple interpolation algorithm which
rapidly converges for an increasing number of known expansion coefficients. The
accuracy is illustrated by calculating the ground state energies of the
anharmonic oscillator using only the leading large-order coefficient $b_0$
(apart from the trivial expansion coefficent $a_0=1/2$). The errors are less
than 0.5 for all g. The algorithm is applied to find energy and mass of the
Fr\"ohlich-Feynman polaron. Our mass is quite different from Feynman's
variational approach.


title: Attaching Theories of Consciousness to Bohmian Quantum Mechanics

abstract:
  The de Broglie-Bohm theory of quantum mechanics (here simply called Bohmian
Mechanics or BM) [1-10] is an augmentation of ``bare'' quantum mechanics (the
bare theory being given by an algebra of operators and a quantum state that
sets the expectation values of these operators) that includes a definite
history or Bohmian trajectory. This definite trajectory gives BM a somewhat
more classical flavor than most other forms of quantum mechanics (QM) (though
the trajectory certainly has highly nonlocal and other nonclassical aspects in
its evolution), but to see whether or not this makes a difference for
observations by conscious beings, one needs to attach theories of conscious
perceptions to BM and other forms of QM. Here I shall propose various forms of
theories of consciousness for BM, which I shall call {\it Sensible Bohmian
Mechanics} (SBM), and compare them with a proposal I have made for a theory of
consciousness attached to bare QM, which I call {\it Sensible Quantum
Mechanics} (SQM) [11-15]. I find that only certain special forms of SBM would
give essentially similar predictions as SQM, though a wider class might be in
practice indistinguishable to any single observer. I also remain sceptical that
a viable complete form of SBM will turn out to be as simple a description of
the universe as a viable complete form of SQM, but of course it is too early to
know yet what the form of the simplest complete theory of our universe is.


title:
The Leading Order of the Theory of Strong Perturbations in Quantum
  Mechanics

abstract:
  We prove that, for a quantum system that undergoes a strong perturbation, the
solution of the leading order equation of the strong field approximation
(M.Frasca, Phys. Rev. A, {\bf 45}, 43 (1992)) can be derived by the adiabatic
approximation. In fact, it is shown that greatest is the perturbation and more
similar the quantum system is to an adiabatic one, the solution being written
as a superposition of eigenstates of the time-dependent perturbation.A direct
consequence of this result is that the solution of the Schr\"{o}dinger equation
in the interaction picture, in the same approximation for the perturbation,
coincides with the one of the leading order of the strong field approximation.
The limitation due to the requirement that the perturbation has to commute at
different times is so overcome. Computational difficulties could arise to go to
higher orders. Beside, the method is not useful for perturbations that are
constant in time. In such a case a small time series is obtained, indicating
that this approximation is just an application to quantum mechanics of the
Kirkwood-Wigner expansion of statistical mechanics. The theory obtained in this
way is applied to a time-dependent two-level spin model, already considered for
the study of the Berry's phase, showing that a geometrical phase could arise if
a part of the hamiltonian is considered as a strong perturbation. No adiabatic
approximation is taken on the parameters of the hamiltonian, while their
cyclicity is retained.


title: Minimum Decision Cost for Quantum Ensembles

abstract:
  For a given ensemble of $N$ independent and identically prepared particles,
we calculate the binary decision costs of different strategies for measurement
of polarised spin 1/2 particles. The result proves that, for any given values
of the prior probabilities and any number of constituent particles, the cost
for a combined measurement is always less than or equal to that for any
combination of separate measurements upon sub-ensembles. The Bayes cost, which
is that associated with the optimal strategy (i.e., a combined measurement) is
obtained in a simple closed form.


title:
Variational Resummation of Divergent Series with known Large-Order
  Behavior

abstract:
  Recently-developed variational perturbation expansions converge exponentially
fast for positive coupling constants. They do not, however, possess the correct
left-hand cut in the complex coupling constant plane, implying a wrong
large-order behavior of their Taylor expansion coefficients. We correct this
deficiency and present a method of resumming divergent series with their proper
large-order behavior. For a given set of expansion coefficients, knowledge of
the large-order behavior considerably improves the quality of the
approximation.


title: Exact semiclassical wave equation for stochastic quantum optics

abstract:
  Semiclassical (stochastic) wave equations are proposed for the coupled
dynamics of atomic quantum states and semiclassical radiation field. All
relevant predictions of standard unitary quantum dynamics are exactly
reproducible in the framework of stochastic wave equation model. We stress in
such a way that the concept of stochastic wave equations is not to be
restricted to the widely used Markovian approximation.


title:
Classical Dynamics for Linear Systems: The Case of Quantum Brownian
  Motion

abstract:
  It has long been recognized that the dynamics of linear quantum systems is
classical in the Wigner representation. Yet many conceptually important linear
problems are typically analyzed using such generally applicable techniques as
influence functionals and Bogoliubov transformations. In this Letter we point
out that the classical equations of motion provide a simpler and more intuitive
formalism for linear quantum systems. We examine the important problem of
Brownian motion in the independent oscillator model, and show that the quantum
dynamics is described directly and completely by a c-number Langevin equation.
We are also able to apply recent insights into quantum Brownian motion to show
that the classical Fokker-Planck equation is always local in time, regardless
of the spectral density of the environment.


title: Optical scattering angles and Bose-stimulated motion in cold atomic gas

abstract:
  Bose statistics imply a substantial enhancement at small angles for light
scattering off a cold, Bose gas. The enhancement increases dramatically at the
Bose-Einstein temperature. This phenomenon could be utilized to eliminate
almost entirely the heating of the gas by a weak probe light beam.


title: Building scars for integrable systems

abstract:
  It is shown, by means of a simple specific example, that for integrable
systems it is possible to build up approximate eigenfunctions, called {\it
asymptotic eigenfunctions}, which are concentrated as much as one wants to a
classical trajectory and have a lifetime as long as one wants. These states are
directly related to the presence of shell structures in the quantal spectrum of
the system. It is argued that the result can be extended to classically chaotic
system, at least in the asymptotic regime.


title: How to Measure a Beable

abstract:
  A brief discussion is given of measurement within the context of a theory of
"beables", e.g. theories of de Broglie, Bohm, Bell, Vink, and also "modal"
theories. It is shown that even in an ideal von Neumann measurement of a
beable, the measured value may not agree with the value which the beable had
prior to the measurement.


title: Jamming non-local quantum correlations

abstract:
  We present a possible scheme to tamper with non-local quantum correlations in
a way that is consistent with relativistic causality, but goes beyond quantum
mechanics. A non-local ``jamming" mechanism, operating within a certain
space-time window, would not violate relativistic causality and would not lead
to contradictory causal loops. The results presented in this Letter do not
depend on any model of how quantum correlations arise and apply to any jamming
mechanism.


title:
On Galilei Invariance in Quantum Mechanics and the Bargmann
  Superselection Rule

abstract:
  We reinvestigate Bargmann's superselection rule for the overall mass of $n$
particles in ordinary quantum mechanics with Galilei invariant interaction
potential. We point out that in order for mass to define a superselection rule
it should be considered as a dynamical variable. We present a minimal extension
of the original dynamics in which mass it treated as dynamical variable. Here
the classical symmetry group turns out to be given by an $\reals$-extension of
the Galilei group which formerly appeared only at the quantum level. There is
now no obstruction to implement an action of the classical symmetry group on
Hilbert space. We include some critical comments of a general nature on formal
derivations of superselection rules without dynamical context.


title:
Recurrence-shift relations for the polynomial functions of Aldaya,
  Bisquert, and Navarro-Salas

abstract:
  Using a simple factorization scheme we obtain the recurrence-shift relations
of the polynomial functions of Aldaya, Bisquert and Navarro-Salas (ABNS),
F_n^N(\frac\omega c\sqrtN x), i.e., one-step first-order differential relations
referring to N, as follows. Firstly, we apply the scheme to the polynomial
degree confirming the recurrence relations of Aldaya, Bisquert and
Navarro-Salas, but also obtaining another slightly modified pair. Secondly, the
factorization scheme is applied to the Gegenbauer polynomials to get the
recurrence relations with respect to their parameter. Next, we make use of
Nagel's result, showing the connection between Gegenbauer polynomials and the
ABNS functions, to write down the recurrence-shift relations for the latter
ones. Such relations may be used in the study of the spatial structure of
pair-creation processes in an Anti-de Sitter gravitational background


title:
Alternative Derivation of the Hu-Paz-Zhang Master Equation for Quantum
  Brownian Motion

abstract:
  Hu, Paz and Zhang [ B.L. Hu, J.P. Paz and Y. Zhang, Phys. Rev. D {\bf 45}
(1992) 2843] have derived an exact master equation for quantum Brownian motion
in a general environment via path integral techniques. Their master equation
provides a very useful tool to study the decoherence of a quantum system due to
the interaction with its environment. In this paper, we give an alternative and
elementary derivation of the Hu-Paz-Zhang master equation, which involves
tracing the evolution equation for the Wigner function. We also discuss the
master equation in some special cases.


title: Primality Test Via Quantum Factorization

abstract:
  We consider a probabilistic quantum implementation of a variable of the
Pocklington-Lehmer $N-1$ primality test using Shor's algorithm. O($\log^3 N
\log\log N \log\log\log N$) elementary q-bit operations are required to
determine the primality of a number $N$, making it (asymptotically) the fastest
known primality test. Thus, the potential power of quantum mechanical computers
is once again revealed.


title: Approximation by Quantum Circuits

abstract:
  In a recent preprint by Deutsch et al. [1995] the authors suggest the
possibility of polynomial approximability of arbitrary unitary operations on
$n$ qubits by 2-qubit unitary operations. We address that comment by proving
strong lower bounds on the approximation capabilities of g-qubit unitary
operations for fixed g. We consider approximation of unitary operations on
subspaces as well as approximation of states and of density matrices by quantum
circuits in several natural metrics. The ability of quantum circuits to
probabilistically solve decision problem and guess checkable functions is
discussed. We also address exact unitary representation by reducing the upper
bound by a factor of n^2 and by formalizing the argument given by Barenco et
al. [1995] for the lower bound. The overall conclusion is that almost all
problems are hard to solve with quantum circuits.


title: Bounds for Approximation in Total Variation Distance by Quantum Circuits

abstract:
  It was recently shown that for reasonable notions of approximation of states
and functions by quantum circuits, almost all states and functions are
exponentially hard to approximate [Knill 1995]. The bounds obtained are
asymptotically tight except for the one based on total variation distance
(TVD). TVD is the most relevant metric for the performance of a quantum
circuit. In this paper we obtain asymptotically tight bounds for TVD. We show
that in a natural sense, almost all states are hard to approximate to within a
TVD of 2/e-\epsilon even for exponentially small \epsilon. The quantity 2/e is
asymptotically the average distance to the uniform distribution. Almost all
states with probability amplitudes concentrated in a small fraction of the
space are hard to approximate to within a TVD of 2-\epsilon. These results
imply that non-uniform quantum circuit complexity is non-trivial in any
reasonable model. They also reinforce the notion that the relative information
distance between states (which is based on the difficulty of transforming one
state to another) fully reflects the dimensionality of the space of qubits, not
the number of qubits.


title: Quantum cryptography based on Wheeler's delayed choice experiment

abstract:
  We describe a cryptographic protocol in which Wheeler's delayed choice
experiment is used to generate the key distribution. The protocol, which uses
photons polarized only along one axis, is secure against general attacks.


title: Nonlocality as an axiom for quantum theory

abstract:
  Quantum mechanics and relativistic causality together imply nonlocality:
nonlocal correlations (that violate the CHSH inequality) and nonlocal equations
of motion (the Aharonov-Bohm effect). Can we invert the logical order? We
consider a conjecture that nonlocality and relativistic causality together
imply quantum mechanics. We show that correlations preserving relativistic
causality can violate the CHSH inequality more strongly than quantum
correlations. Also, we describe nonlocal equations of motion, preserving
relativistic causality, that do not arise in quantum mechanics. In these
nonlocal equations of motion, an experimenter ``jams" nonlocal correlations
between quantum systems.


title: More About Tunnelling Times, the Dwell Time, and the ``Hartman Effect"

abstract:
  In a recent review paper [{\em Phys. Reports} {\bf 214} (1992) 339] we
proposed, within conventional quantum mechanics, new definitions for the
sub-barrier tunnelling and reflection times. \ Aims of the present paper are: \
(i) presenting and analysing the results of various numerical calculations
(based on our equations) on the penetration and return times $<\tau_{\, \rm
Pen}>$, $<\tau_{\, \rm Ret}>$, during tunnelling {\em inside} a rectangular
potential barrier, for various penetration depths $x_{\rm f}$; \ (ii) putting
forth and discussing suitable definitions, besides of the mean values, also of
the {\em variances} (or dispersions) ${\rm D} \, {\tau_{\rm T}}$ and ${\rm D}
\, {\tau_{\, \rm R}}$ for the time durations of transmission and reflection
processes; \ (iii) mentioning, moreover, that our definition $<\tau_{\rm T}>$
for the average transmission time results to constitute an {\em improvement} of
the ordinary dwell--time ${\ove \tau}^{\rm Dw}$ formula: \ (iv) commenting, at
last, on the basis of our {\em new} numerical results, upon some recent
criticism by C.R.Leavens. \ \ We stress that our numerical evaluations {\em
confirm} that our approach implied, and implies, the existence of the {\em
Hartman effect}: an effect that in these days (due to the theoretical
connections between tunnelling and evanescent--wave propagation) is receiving
---at Cologne, Berkeley, Florence and Vienna--- indirect, but quite
interesting, experimental verifications. \ Eventually, we briefly analyze some
other definitions of tunnelling times.


title: Quantum Mechanics On Spaces With Finite Fundamental Group

abstract:
  We consider in general terms dynamical systems with finite-dimensional,
non-simply connected configuration-spaces. The fundamental group is assumed to
be finite. We analyze in full detail those ambiguities in the quantization
procedure that arise from the non-simply connectedness of the classical
configuration space. We define the quantum theory on the universal cover but
restrict the algebra of observables $\O$ to the commutant of the algebra
generated by deck-transformations. We apply standard superselection principles
and construct the corresponding sectors. We emphasize the relevance of all
sectors and not just the abelian ones.


title: Quantum Computing and Phase Transitions in Combinatorial Search

abstract:
  We introduce an algorithm for combinatorial search on quantum computers that
is capable of significantly concentrating amplitude into solutions for some NP
search problems, on average. This is done by exploiting the same aspects of
problem structure as used by classical backtrack methods to avoid unproductive
search choices. This quantum algorithm is much more likely to find solutions
than the simple direct use of quantum parallelism. Furthermore, empirical
evaluation on small problems shows this quantum algorithm displays the same
phase transition behavior, and at the same location, as seen in many previously
studied classical search methods. Specifically, difficult problem instances are
concentrated near the abrupt change from underconstrained to overconstrained
problems.


title:
Exponential Asymptotics in a Singular Limit for $n$-Level Scattering
  Systems

abstract:
  The singular limit $\eps\ra 0$ of the $S$-matrix associated with the equation
$i\eps d\psi(t)/dt=H(t)\psi(t)$ is considered, where the analytic generator
$H(t)\in M_n(\C)$ is such that its spectrum is real and non-degenerate for all
$t\in\R$. Sufficient conditions allowing to compute asymptotic formulas for the
exponentially small off-diagonal elements of the $S$-matrix as $\eps\ra 0$ are
explicited and a wide class of generators for which these conditions are
verified is defined. These generators are obtained by means of generators whose
spectrum exhibits eigenvalue crossings which are perturbed in such a way that
these crossings turn to avoided crossings. The exponentially small asymptotic
formulas which are derived are shown to be valid up to exponentially small
relative error, by means of a joint application of the complex WKB method
together with superasymptotic renormalization. The application of these results
to the study of quantum adiabatic transitions in the time dependent
Schr\"odinger equation and of the semiclassical scattering properties of the
multichannel stationary Schr\"odinger equation closes this paper. The results
presented here are a generalization to $n$-level systems, $n\geq 2$, of results
previously known for $2$-level systems only.


title: Lorentz-invariant Bohmian Mechanics

abstract:
  A derivation of the Bohm model, and some general comments about it, are
given. A modification of the model which is formally local and
Lorentz-invariant is introduced, and its properties studied for a simple
experiment.


title: Atomic Supersymmetry, Oscillators, and the Penning Trap

abstract:
  This paper begins with some background information and a summary of results
in atomic supersymmetry. The connection between the supersymmetric Coulomb and
oscillator problems in arbitrary dimensions is outlined. Next, I treat the
issue of finding a description of supersymmetry-based quantum-defect theory in
terms of oscillators. A model with an anharmonic term that yields analytical
eigenfunctions is introduced to solve this problem in arbitrary dimensions.
Finally, I show that geonium atoms (particles contained in a Penning trap)
offer a realization of a multidimensional harmonic oscillator in an idealized
limit. The anharmonic theory presented here provides a means of modeling the
realistic case.


title: Can Future Events Influence the Present?

abstract:
  Widom, Srivastava, and Sassaroli have published [Phys. Lett. A 203, 255
(1995)] a calculation which purports to show that "future events can affect
present events". In this note an error in their calculation is identified.


title:
One-particle excitations and bound states in non-relativistic current
  $\times$ current model

abstract:
  Vacuum structure, one-particle excitations' spectra and bound states of these
excitations are studied in frame of non-relativistic quantum field model with
current $\times$ current type interaction. Hidden symmetry of the model is
found. It could be broken or exact depending on the coupling constant value.
The effect of "piercing" vacuum , generating the appearance of heavy fermionic
excitations, could occur in the spontaneously broken phase.


title: Aharonov-Bohm Type Forces Between Magnetic Fluxons

abstract:
  Forces related to A-B phases between fluxons with $\Phi=\alpha\Phi_0\ \ \ $
$\alpha\ne integer$ are discussed. We find a $\alpha^2\ln(r)$ type interaction
screened on a scale $\lambda_s$. The forces exist only when the fluxons are
actually immersed in the region with non vanishing charge density and are
periodic in $\alpha$. We briefly comment on the problem of observing such
forces.


title: Radial Squeezed States and Rydberg Wave Packets

abstract:
  We outline an analytical framework for the treatment of radial Rydberg wave
packets produced by short laser pulses in the absence of external electric and
magnetic fields. Wave packets of this type are localized in the radial
coordinates and have p-state angular distributions. We argue that they can be
described by a particular analytical class of squeezed states, called radial
squeezed states. For hydrogenic Rydberg atoms, we discuss the time evolution of
the corresponding hydrogenic radial squeezed states. They are found to undergo
decoherence and collapse, followed by fractional and full revivals. We also
present their uncertainty product and uncertainty ratio as functions of time.
Our results show that hydrogenic radial squeezed states provide a suitable
analytical description of hydrogenic Rydberg atoms excited by short-pulsed
laser fields.


title: Atomic Supersymmetry, Rydberg Wave Packets, and Radial Squeezed States

abstract:
  We study radial wave packets produced by short-pulsed laser fields acting on
Rydberg atoms, using analytical tools from supersymmetry-based quantum-defect
theory. We begin with a time-dependent perturbative calculation for
alkali-metal atoms, incorporating the atomic-excitation process. This provides
insight into the general wave packet behavior and demonstrates agreement with
conventional theory. We then obtain an alternative analytical description of a
radial wave packet as a member of a particular family of squeezed states, which
we call radial squeezed states. By construction, these have close to minimum
uncertainty in the radial coordinates during the first pass through the outer
apsidal point. The properties of radial squeezed states are investigated, and
they are shown to provide a description of certain aspects of Rydberg atoms
excited by short-pulsed laser fields. We derive expressions for the time
evolution and the autocorrelation of the radial squeezed states, and we study
numerically and analytically their behavior in several alkali-metal atoms. Full
and fractional revivals are observed. Comparisons show agreement with other
theoretical results and with experiment.


title: Quantum space-time fluctuations and primary state diffusion

abstract:
  Nondifferentiable fluctuations in space-time on a Planck scale introduce
stochastic terms into the equations for quantum states, resulting in a proposed
new foundation for an existing alternative quantum theory, primary state
diffusion (PSD). Planck-scale stochastic space-time structure results in
quantum fluctuations, whilst larger-scale curvature is responsible for
gravitational forces. The gravitational field and the quantum fluctuation field
are the same, differing only in scale. The quantum mechanics of small systems,
classical mechanics of large systems and the physics of quantum experiments are
all derived dynamically, without any prior division into classical and quantum
domains, and without any measurement hypothesis. Unlike the earlier derivation
of PSD, the new derivation, based on a stochastic space-time differential
geometry, has essentially no free parameters. However many features of this
structure remain to be determined. The theory is falsifiable in the laboratory,
and critical matter interferometry experiments to distinguish it from ordinary
quantum mechanics may be feasible within the next decade.


title: An Example of the Decoherence Approach to Quantum Dissipative Chaos

abstract:
  Quantum chaos---the study of quantized nonintegrable Hamiltonian systems---is
an extremely well-developed and sophisticated field. By contrast, very little
work has been done in looking at quantum versions of systems which classically
exhibit {\it dissipative} chaos. Using the decoherence formalism of Gell-Mann
and Hartle, I find a quantum mechanical analog of one such system, the forced
damped Duffing oscillator. I demonstrate the classical limit of the system, and
discuss its decoherent histories. I show that using decoherent histories, one
can define not only the quantum map of an entire density operator, but can find
an analog to the Poincar\'e map of the individual trajectory. Finally, I argue
the usefulness of this model as an example of quantum dissipative chaos, as
well as of a practical application of the decoherence formalism to an
interesting problem.


title:
The Higher Orders of the Theory of Strong Perturbations in Quantum
  Mechanics and the Secularity Problem

abstract:
  We solve the higher order equations of the theory of the strong perturbations
in quantum mechanics given in M. Frasca, Phys. Rev. A 45, 43 (1992), by
assuming that, at the leading order, the wave function goes adiabatically. This
is accomplished by deriving the unitary operator of adiabatic evolution for the
leading order. In this way it is possible to show that at least one of the
causes of the problem of phase-mixing, whose effect is the polynomial increase
in time of the perturbation terms normally called secularities, arises from the
shifts of the perturbation energy levels due to the unperturbed part of the
hamiltonian. An example is given for a two-level system that, anyway, shows a
secularity at second order also in the standard theory of small perturbations.
The theory is applied to the quantum analog of a classical problem that can
become chaotic, a particle under the effect of two waves of different
amplitudes, frequencies and wave numbers.


title: Long-Term Evolution and Revival Structure of Rydberg Wave Packets

abstract:
  It is known that, after formation, a Rydberg wave packet undergoes a series
of collapses and revivals within a time period called the revival time, $t_{\rm
rev}$, at the end of which it is close to its original shape. We study the
behavior of Rydberg wave packets on time scales much greater than $t_{\rm
rev}$. We show that after a few revival cycles the wave packet ceases to reform
at multiples of the revival time. Instead, a new series of collapses and
revivals commences, culminating after a time period $t_{\rm sr} \gg t_{\rm
rev}$ with the formation of a wave packet that more closely resembles the
initial packet than does the full revival at time $t_{\rm rev}$. Furthermore,
at times that are rational fractions of $t_{\rm sr}$, the square of the
autocorrelation function exhibits large peaks with periodicities that can be
expressed as fractions of the revival time $t_{\rm rev}$. These periodicities
indicate a new type of fractional revival occurring for times much greater than
$t_{\rm rev}$. A theoretical explanation of these effects is outlined.


title: The Revival Structure of Rydberg Wave Packets Beyond the Revival Time

abstract:
  After a Rydberg wave packet forms, it is known to undergo a series of
collapses and revivals within a time period called the revival time $t_{\rm
rev}$, at the end of which it resembles its original shape. We study the
behavior of Rydberg wave packets on time scales much greater than $t_{\rm
rev}$. We find that after a few revival cycles the wave packet ceases to reform
at multiples of the revival time. Instead, a new series of collapses and
revivals commences, culminating after a time period $t_{\rm sr} \gg t_{\rm
rev}$ with the formation of a wave packet that more closely resembles the
initial packet than does the full revival at time $t_{\rm rev}$. Furthermore,
at times that are rational fractions of $t_{\rm sr}$, we show that the motion
of the wave packet is periodic with periodicities that can be expressed as
fractions of the revival time $t_{\rm rev}$. These periodicities indicate a new
type of fractional revival, occurring for times much greater than $t_{\rm
rev}$. We also examine the effects of quantum defects and laser detunings on
the revival structure of Rydberg wave packets for alkali-metal atoms.


title: Superrevivals of Rydberg Wave Packets

abstract:
  The revival structure and evolution of Rydberg wave packets are studied on a
time scale much greater than the revival time $t_{\rm rev}$. We find a new
level of revival structure and periodic motion different from that of the known
fractional revivals. The new sequence of revivals culminates with the formation
of a wave packet that more closely resembles the initial packet than does the
full revival at time $t_{\rm rev}$. We refer to such a revival as a
superrevival. We also show that an initial radial wave packet may be described
as a type of squeezed state known as a radial squeezed state. Our results apply
not only for hydrogenic wave packets, but for wave packets in alkali-metal
atoms as well in the context of quantum defect theory.


title:
Polynomial-Time Algorithms for Prime Factorization and Discrete
  Logarithms on a Quantum Computer

abstract:
  A digital computer is generally believed to be an efficient universal
computing device; that is, it is believed able to simulate any physical
computing device with an increase in computation time of at most a polynomial
factor. This may not be true when quantum mechanics is taken into
consideration. This paper considers factoring integers and finding discrete
logarithms, two problems which are generally thought to be hard on a classical
computer and have been used as the basis of several proposed cryptosystems.
Efficient randomized algorithms are given for these two problems on a
hypothetical quantum computer. These algorithms take a number of steps
polynomial in the input size, e.g., the number of digits of the integer to be
factored.


title: Non-classical Photon Statistics For Two-mode Optical Fields

abstract:
  The non-classical property of subpoissonian photon statistics is extended
from one to two-mode electromagnetic fields, incorporating the physically
motivated property of invariance under passive unitary transformations.
Applications to squeezed coherent states, squeezed thermal states, and
superposition of coherent states are given. Dependences of extent of
non-classical behaviour on the independent squeezing parameters are graphically
displayed.


title: The Real Symplectic Groups in Quantum Mechanics and Optics

abstract:
  text of abstract (We present a utilitarian review of the family of matrix
groups $Sp(2n,\Re)$, in a form suited to various applications both in optics
and quantum mechanics. We contrast these groups and their geometry with the
much more familiar Euclidean and unitary geometries. Both the properties of
finite group elements and of the Lie algebra are studied, and special attention
is paid to the so-called unitary metaplectic representation of $Sp(2n,\Re)$.
Global decomposition theorems, interesting subgroups and their generators are
described. Turning to $n$-mode quantum systems, we define and study their
variance matrices in general states, the implications of the Heisenberg
uncertainty principles, and develop a U(n)-invariant squeezing criterion. The
particular properties of Wigner distributions and Gaussian pure state
wavefunctions under $Sp(2n,\Re)$ action are delineated.)


title: Quantum Cryptography with Orthogonal States?

abstract: This is a Comment on Phys Rev Lett 75 (1995) 1239, by Goldenberg and Vaidman


title: Quantum Mechanics as an Exotic Probability Theory

abstract:
  Recent results suggest that quantum mechanical phenomena may be interpreted
as a failure of standard probability theory and may be described by a Bayesian
complex probability theory.


title:
Convergence behavior of variational perturbation expansion-- A method
  for locating Bender-Wu singularities

abstract:
  Variational perturbation expansions have recently been used to calculate
directly the strong-coupling expansion coefficients of the anharmonic
oscillator. The convergence is exponentially fast with superimposed
oscillations, as recently observed empirically by the authors. In this note,
the observed behavior is explained and used to determine accurately the
magnitude and phase of the leading Bender-Wu singularity which is responsible
for the finite convergence radius in the complex coupling constant plane.


title:
Altered Stats: Two anyons via path integrals for multiply connected
  spaces

abstract:
  We apply the formalism of path integrals in multiply connected spaces to the
problem of two anyons.


title:
Trapped ions in the strong excitation regime: ion interferometry and
  non--classical states

abstract:
  The interaction of a trapped ion with a laser beam in the strong excitation
regime is analyzed. In this regime, a variety of non--classical states of
motion can be prepared either by using laser pulses of well defined area, or by
an adiabatic passage scheme based on the variation of the laser frequency. We
show how these states can be used to investigate fundamental properties of
quantum mechanics. We also study possible applications of this system to build
an ion interferometer.


title: Coherent States for Isospectral Hamiltonians

abstract:
  We show that for the strictly isospectral Hamiltonians, the corresponding
coherent states are related by a unitary transformation. As an illustration, we
discuss, the example of strictly isospectral one-dimensional harmonic
oscillator Hamiltonians and the associated coherent states.


title: Global existence and uniqueness of Bohmian trajectories

abstract:
  It is shown that Bohmian mechanics is internally consistent in the sense that
the equations of motion typically have global solutions despite the fact that
the velocity field is singular at the nodes of the wave function and at other
points. This result is fundamental for the derivation of the quantum formalism.
The role of the quantum flux is emphasized.


title: Elliptical Squeezed States and Rydberg Wave Packets

abstract:
  We present a theoretical construction for closest-to-classical wave packets
localized in both angular and radial coordinates and moving on a keplerian
orbit. The method produces a family of elliptical squeezed states for the
planar Coulomb problem that minimize appropriate uncertainty relations in
radial and angular coordinates. The time evolution of these states is studied
for orbits with different semimajor axes and eccentricities. The elliptical
squeezed states may be useful for a description of the motion of Rydberg wave
packets excited by short-pulsed lasers in the presence of external fields,
which experiments are attempting to produce. We outline an extension of the
method to include certain effects of quantum defects appearing in the
alkali-metal atoms used in experiments.


title: Scattering Theory from a Bohmian Perspective

abstract:
  Quantum mechanical scattering theory is a subject with a long and winding
history. We shall pick out some of the most important concepts and ideas of
scattering theory and look at them from the perspective of Bohmian mechanics:
Bohmian mechanics, having real particle trajectories, provides an excellent
basis for analyzing scattering phenomena.


title: Quantum Mechanics as a Classical Theory VI: The Classical Spin

abstract:
  In these continuation papers (VI and VII) we are interested in approach the
problem of spin from a classical point of view. In this first paper we will
show that the spin is neither basically relativistic nor quantum but reflects
just a simmetry property related to the Lie algebra to which it is associated.
The classical approach will be paraleled with the usual quantum one to stress
their formal similarities and epistemological differences. The important
problem of Einstein-Bose condensation for fermions will also be addressed.


title:
Quantum Mechanics as a Classical Theory VII: The Classical Spin
  Eigenfunctions

abstract:
  In this continuation paper the Schr\"odinger equation for the half-integral
spin eigenfunctions is obtained and solved. We show that all the properties
already derived using the Heisemberg matrix calculation and Pauli's matrices
are also obtained in the realm of these analytical functions. We also show that
Einstein-Bose condensation for fermions is expected. We then conclude this
series of two papers on the concept of classical spin.


title: Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

abstract:
  `Umbral calculus' deals with representations of the canonical commutation
relations. We present a short exposition of it and discuss how this calculus
can be used to discretize continuum models and to construct representations of
Lie algebras on a lattice. Related ideas appeared in recent publications and we
show that the examples treated there are special cases of umbral calculus. This
observation then suggests various generalizations of these examples. A special
umbral representation of the canonical commutation relations given in terms of
the position and momentum operator on a lattice is investigated in detail.


title: Quantum chaos in open systems: a quantum state diffusion analysis

abstract:
  Except for the universe, all quantum systems are open, and according to
quantum state diffusion theory, many systems localize to wave packets in the
neighborhood of phase space points. This is due to decoherence from the
interaction with the environment, and makes the quasiclassical limit of such
systems both more realistic and simpler in many respects than the more familiar
quasiclassical limit for closed systems. A linearized version of this theory
leads to the correct classical dynamics in the macroscopic limit, even for
nonlinear and chaotic systems. We apply the theory to the forced, damped
Duffing oscillator, comparing the numerical results of the full and linearized
equations, and argue that this can be used to make explicit calculations in the
decoherent histories formalism of quantum mechanics.


title: Temporal behavior of quantum mechanical systems

abstract:
  The temporal behavior of quantum mechanical systems is reviewed. We study the
so-called quantum Zeno effect, that arises from the quadratic short-time
behavior, and the analytic properties of the ``survival" amplitude. It is shown
that the exponential behavior is due to the presence of a simple pole in the
second Riemannian sheet, while the contribution of the branch point yields a
power behavior for the amplitude. The exponential decay form is cancelled at
short times and dominated at very long times by the branch-point contributions,
which give a Gaussian behavior for the former and a power behavior for the
latter. In order to realize the exponential law in quantum theory, it is
essential to take into account a certain kind of macroscopic nature of the
total system. Some attempts at extracting the exponential decay law from
quantum theory, aiming at the master equation, are briefly reviewed, including
van Hove's pioneering work and his well-known ``$\lambda^2T$" limit. We clarify
these general arguments by introducing and studying a solvable dynamical model.
Some implications for the quantum measurement problem are also discussed, in
particular in connection with dissipation.


title: Penning trap and vacuum noise

abstract:
  A number of comments are provided on Rogers's model experiment to measure the
circular Unruh vacuum noise by means of a hyperbolic Penning trap inside a
microwave cavity. It is suggested that cylindrical Penning traps, being
geometrically simpler, and controlled almost at the same level of accuracy as
the hyperbolic trap, might be a better choice for such an experiment. Besides,
the microwave modes of the trap itself, of known analytical structure, can be
directly used in trying to obtain measurable results for such a tiny noise
effect.


title: Introduction to Quantum Optics

abstract:
  The theory of quantum propagator and time--dependent integrals of motion in
quantum optics is reviewed as well as the properties of Wigner function,
Q--function, and coherent state representation. Propagators and wave functions
of a free particle, harmonic oscillator, and the oscillator with varying
frequency are studied using time--dependent linear in position and momentum
integrals of motion. Such nonclassical states of light (of quantum systems) as
squeezed states, correlated states, even and odd coherent states (Schr\"odinger
cat states) are considered. Photon distribution functions of Schr\"odinger cat
male and female states are given, and the photon distribution function of
squeezed vacuum is derived using the theory of the oscillator with varying
parameters. Properties of multivariable Hermite polynomials used for the
description of the multimode squeezed and correlated light and polymode
Schr\"odinger cats are studied.


title:
Off-Diagonal Long-Range Order, Restricted Gauge Transformations, and
  Aharonov-Bohm Effect in Conductors

abstract:
  The Hamiltonian describing a conductor surrounding an external magnetic field
contains a nonvanishing vector potential in the volume accessible to the
electrons and nuclei of which the conductor is made. That vector potential
cannot be removed by a gauge transformation. Nevertheless, a macroscopic normal
conductor can experience no Aharonov-Bohm effect. That is proved by assuming
only that a normal conductor lacks off-diagonal long-range order (ODLRO). Then
by restricting the Hilbert space to density matrices which lack ODLRO, it is
possible to introduce a restricted gauge transformation that removes the
interaction of the conductor with the vector potential.


title:
Comment on 'Reduced System Dynamics from the N-Body Schrodinger
  Equation'

abstract:
  We argue that the "reduced wave function", proposed recently [Phys.Rev.Lett.
{\bf 75}, 2255 (1995)], contains conditional and restricted information on the
reduced system. The concept of "reduced wave function" can thus not represent a
relevant alternative to the common reduced dynamics methods.


title: Schr\"odinger's Cat -- Amended

abstract:
  Arguments have been raised that the system--observer cut of quantum mechanics
can be shifted arbitrarily close to, or even into, the conscious observer. Here
I show that this view leads to {\it observable} contradictions (despite our
inability to control the phases of macroscopic states). For this purpose I
modify and extend Schr\"odinger's well--known superposition of a cat in its
dead and alive state. Implications for other interpretations of quantum
mechanics are also discussed. My conclusion is that quantum mechanics is
incomplete. The question ``When does the state vector collapse?'' seems to be
unavoidable, has observable consequences, and is not answered by quantum
mechanics.


title:
Squeezed States for General Multiphoton Systems: Towards the
  displacement-operator formalism

abstract:
  We propose a displacement-operator approach to some aspects of squeezed
states for general multiphoton systems. The explicit displacement-operators of
the squeezed vacuum and the coherent states are achieved and expresses as the
ordinary exponential form. As a byproduct the coherent states of the
$q$-oscillator are obtained by the {\it usual exponential}
displacement-operator.


title: Branching Space-time analysis of the GHZ theorem

abstract:
  Greenberger, Horne, Shimony and Zeilinger gave a new version of the Bell
theorem without using inequalities (probabilities). Mermin summarized it
concisely; but Bohm and Hiley criticized Mermin's proof from contextualists'
point of view.
  Using the Branching Space-time language, in this paper a proof will be given
that is free of these difficulties. At the same time we will also clarify the
limits of the validity of the theorem when it is taken as a proof that quantum
mechanics is not compatible with a deterministic world nor with a world that
permits correlated space-related events without a common cause.


title:
On a possible connection of non-critical strings to certain aspects of
  quantum brain function

abstract:
  We review certain aspects of brain function which could be associated with
non-critical (Liouville) string theory. In particular we simulate the physics
of brain microtubules (MT) by using a (completely integrable) non-critical
string, we discuss the collapse of the wave function as a result of quantum
gravity effects due to abrupt conformational changes of the MT protein dimers,
and we propose a new mechanism for memory coding.


title: The Real Significance of the Electromagnetic Potentials

abstract:
  The importance of the potential is revealed in a newly discovered effect of
the potential. This paper explore the same issue introduced in quant-ph/9506038
from several different aspects including electron optics and relativity. Some
people fail to recognize this effect due to a wrong application of gauge
invariance.


title: Quantum algorithmic information theory

abstract:
  The agenda of quantum algorithmic information theory, ordered `top-down,' is
the quantum halting amplitude, followed by the quantum algorithmic information
content, which in turn requires the theory of quantum computation. The
fundamental atoms processed by quantum computation are the quantum bits which
are dealt with in quantum information theory. The theory of quantum computation
will be based upon a model of universal quantum computer whose elementary unit
is a two-port interferometer capable of arbitrary $U(2)$ transformations. Basic
to all these considerations is quantum theory, in particular Hilbert space
quantum mechanics.


title: Solving the Coulomb Schrodinger Equation in d=2+1 via Sinc Collocation

abstract:
  We solve the non-relativistic Coulomb Shrodinger equation in d = 2+1 via sinc
collocation. We get excellent convergence using a generalized sinc basis set in
position space. Since convergence in position space could not be obtained with
more common numerical techniques, this result helps to corroborate the
conjecture that the use of a localized basis set within the context of light
cone quantization can yield much better convergence. All of the computations
presented here were performed on an IBM-compatible PC with an Intel 486DX2-66
microchip.


title:
Proposal for an experimental test of the many-worlds interpretation of
  quantum mechanics

abstract:
  The many-worlds interpretation of quantum mechanics predicts the formation of
distinct parallel worlds as a result of a quantum mechanical measurement.
Communication among these parallel worlds would experimentally rule out
alternatives to this interpretation. A procedure for ``interworld'' exchange of
information and energy, using only state of the art quantum optical equipment,
is described. A single ion is isolated from its environment in an ion trap.
Then a quantum mechanical measurement with two discrete outcomes is performed
on another system, resulting in the formation of two parallel worlds. Depending
on the outcome of this measurement the ion is excited from only one of the
parallel worlds before the ion decoheres through its interaction with the
environment. A detection of this excitation in the other parallel world is
direct evidence for the many-worlds interpretation. This method could have
important practical applications in physics and beyond.


title: Geometric Quantization from a Coherent State Viewpoint

abstract:
  A fully geometric procedure of quantization that utilizes a natural and
necessary metric on phase space is reviewed and briefly related to the goals of
the program of geometric quantization.


title: Spontaneous Fermion Production by a Supercritical Potential Well

abstract:
  A second quantised theory of electrons and positrons in a deep time-dependent
potential well is discussed. It is shown that positron production from the well
is a natural consequence of Dirac's hole theory when the strength of the well
becomes supercritical. A formalism is developed whereby the amplitude for
emission of a positron of a given momentum can be calculated. The difference
between positron production and electron-positron pair production is
demonstrated. Considerations of the vacuum charge and of Levinson's theorem are
required for a full description of the problem.


title: A Particle Theory of the Casimir Effect

abstract:
  In previous works Suppes and de Barros used a pure particle model to derive
interference effects, where individual photons have well-defined trajectories,
and hence no wave properties. In the present paper we extend that description
to account for the Casimir effect. We consider that the linear momentum
$\sum\frac{1}{2}\hbar {\bf k}$ of the vacuum state in quantum electrodynamics
corresponds to the linear momentum of virtual photons. The Casimir effect, in
the cases of two parallel plates and the solid ball, is explained in terms of
the pressure caused by the photons. Contrary to quantum electrodynamics, we
assume a finite number of virtual photons.


title: Isolation and Expulsion of Divergences in Quantum Field Theory

abstract:
  Divergences that arise in the quantization of scalar quantum field models by
means of a lattice-space functional integration may be attributed to a single
integration variable, and this fact is demonstrated by showing that if the
integrand for that single integration variable is appropriately changed, then a
perturbation expansion becomes order-by-order finite and divergence free. The
paper concludes with a brief review of a current proposal of how an auxiliary,
nonclassical potential added to the lattice action of a relativistic scalar
field quantization may automatically render an analogous change of the
integrand, and thus may lead, as well, to nontrivial and divergence-free
results.


title: Simple Proof of Invariance of the Bargmann-Wigner Scalar Products

abstract:
  An explicitly covariant formalism for dealing with Bargmann-Wigner fields is
developed. An invariance of the Barmann-Wigner norm can be proved in a unified
way for both massive and massless fields. It is shown that there exists some
freedom in the choice of the form of the Bargmann-Wigner scalar product.


title: Squeezed Vacuum Interferometry

abstract:
  A high-sensitive interferometric scheme is presented. It is based on homodyne
detection and squeezed vacuum phase properties. The resulting phase sensitivity
scales as $\delta\phi \simeq {1/4} \bar{n}^{-1}$ with respect to input photons
number.


title: Reconstructing the density operator via simple projectors

abstract:
  We describe the representation of arbitrary density operators in terms of
expectation values of simple projection operators. Two representations are
presented which yield non--recursive schemes for experimentally determining the
density operator of any quantum system. We suggest a possible experimental
implementation in quantum optics.


title:
Empirical logic of finite automata: microstatements versus
  macrostatements

abstract:
  We compare the two approaches to the empirical logic of automata. The first,
called partition logic (logic of microstatements), refers to experiments on
individual automata. The second one, the logic of simulation (logic of
macrostatements), deals with ensembles of automata.


title:
Nuclear recoil corrections to the $2p_\frac{3}{2}$ state energy of
  hydrogen-like and high $Z$ lithium like atoms in all orders in $\alpha Z$

abstract:
  The relativistic nuclear recoil corrections to the energy of the
$2p_{\frac{3}{2}}$ state of hydrogen-like and the $(1s)^{2}2p_{\frac{3}{2}}$
state of 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 total
nuclear recoil contribution to the energy of the $(1s)^{2}2p_{\frac{3}{2}}-
(1s)^{2}2s$ transition in lithium-like uranium constitutes $-0.09\,eV$.


title: Physics and Consciousness

abstract:
  Some contributions of physics towards the understanding of consciousness are
described. As recent relevant models, associative memory neural networks are
mentioned. It is shown that consciousness and quantum physics share some
properties. Two existing quantum models are discussed.


title: Generalized Kochen-Specker Theorem

abstract:
  A generalized Kochen-Specker theorem is proved. It is shown that there exist
sets of $n$ projection operators, representing $n$ yes-no questions about a
quantum system, such that none of the $2^n$ possible answers is compatible with
sum rules imposed by quantum mechanics. Namely, if a subset of commuting
projection operators sums up to a matrix having only even or only odd
eigenvalues, the number of ``yes'' answers ought to be even or odd,
respectively. This requirement may lead to contradictions. An example is
provided, involving nine projection operators in a 4-dimensional space.


title:
Axiomatic foundations of quantum mechanics revisited: the case for
  systems

abstract:
  We present an axiomatization of non-relativistic Quantum Mechanics for a
system with an arbitrary number of components. The interpretation of our system
of axioms is realistic and objective. The EPR paradox and its relation with
realism is discussed in this framework. It is shown that there is no
contradiction between realism and recent experimental results.


title:
Axiomatic Foundations of Nonrelativistic Quantum Mechanics: A Realistic
  Approach

abstract:
  A realistic axiomatic formulation of nonrelativistic quantum mechanics for a
single microsystem with spin is presented, from which the most important
theorems of the theory can be deduced. In comparison with previous
formulations, the formal aspect has been improved by the use of certain
mathematical theories, such as the theory of equipped spaces, and group theory.
The standard formalism is naturally obtained from the latter, starting from a
central primitive concept: the Galilei group.


title: Decoherence of Quantum Fields: Pointer States and Predictability

abstract:
  We study environmentally induced decoherence of an electromagnetic field in a
homogeneous, linear, dielectric medium. We derive an independent oscillator
model for such an environment, which is sufficiently realistic to encompass
essentially all of linear physical optics. Applying the ``predictability
sieve'' to the quantum field, and introducing the concept of a ``quantum
halo'', we recover the familiar dichotomy between background field
configurations and photon excitations around them. We are then able to explain
why a typical linear environment for the electromagnetic field will effectively
render the former classically distinct, but leave the latter fully quantum
mechanical. Finally, we suggest how and why quantum matter fields should suffer
a very different form of decoherence.


title: The Classical Schrodinger's Equation

abstract:
  A non perturbative numerical method for determining the discrete spectra is
deduced from the classical analogue of the Schrodinger's equation. The energy
eigenvalues coincide with the bifurcation parameters for the classical orbits.


title: Keplerian Squeezed States and Rydberg Wave Packets

abstract:
  We construct minimum-uncertainty solutions of the three-dimensional
Schr\"odinger equation with a Coulomb potential. These wave packets are
localized in radial and angular coordinates and are squeezed states in three
dimensions. They move on elliptical keplerian trajectories and are appropriate
for the description of the corresponding Rydberg wave packets, the production
of which is the focus of current experimental effort. We extend our analysis to
incorporate the effects of quantum defects in alkali-metal atoms, which are
used in experiments.


title: Axiomatic Quantum Theory

abstract:
  A rough overview is given over the most essential structures underlying all
working quantum theoretical models as well as axiomatic and algebraic quantum
field theory .


title:
Generalized Unruh effect and Lamb shift for atoms on arbitrary
  stationary trajectories

abstract:
  We study the spontaneous de-excitation and excitation of accelerated atoms on
arbitrary stationary trajectories (``generalized Unruh effect''). We consider
the effects of vacuum fluctuations and radiation reaction separately. We show
that radiation reaction is generally not altered by stationary acceleration,
whereas the contribution of vacuum fluctuations differs for all stationary
accelerated trajectories from its inertial value. Spontaneous excitation from
the ground state occurs for all { accelerated stationary} trajectories and is
therefore the ``normal case''. We furthermore show that the radiative energy
shift (``Lamb shift'') of a two-level atom is modified by acceleration for all
stationary trajectories. Again only vacuum fluctuations give rise to the shift.
Our results are illustrated for the special case of an atom in circular motion,
which may be experimentally relevant.


title:
Quantum decoherence and an adiabatic process in macroscopic and
  mesoscopic systems

abstract:
  Quantum decoherence is of primary importance for relaxation to an equilibrium
distribution and, accordingly, for equilibrium processes. We demonstrate how
coherence breaking implies evolution to a microcanonical distribution
(``microcanonical postulate'') and, on that ground, consider an adiabatic
process, in which there is no thermostat. We stress its difference from a
zero-polytropic process, i.e., a process with zero heat capacity but involving
a thermostat. We find the distribution for the adiabatic process and show that
(i) in the classical limit this distribution is canonical, (ii) for macroscopic
systems, the mean values of energy for adiabatic and zero-polytropic processes
are the same, but its fluctuations are different, and (iii) in general,
adiabatic and zero-polytropic processes are different, which is particularly
essential for mesoscopic systems; for those latter, an adiabatic process is in
general irreversible.


title: EPR-Bell Nonlocality, Lorentz Invariance, and Bohmian Quantum Theory

abstract:
  We discuss the problem of finding a Lorentz invariant extension of Bohmian
mechanics. Due to the nonlocality of the theory there is (for systems of more
than one particle) no obvious way to achieve such an extension. We present a
model invariant under a certain limit of Lorentz transformations, a limit
retaining the characteristic feature of relativity, the non-existence of
absolute time resp. simultaneity. The analysis of this model exemplifies an
important property of any Bohmian quantum theory: the quantum equilibrium
distribution $\rho = |\psi |^2$ cannot simultaneously be realized in all
Lorentz frames of reference.


title: A True Equation to Couple Classical and Quantum Dynamics

abstract:
  Starting from the Schr\"odinger-equation of a composite system, we derive
unified dynamics of a classical harmonic system coupled to an arbitrary
quantized system. The classical subsystem is described by random phase-space
coordinates entangled with the quantized variables of the complementary
subsystem. Our semiclassical equation is {\it true} in a sense that its
predictions are identical to those of the fully quantized composite dynamics.
This exact method applies to a broad class of theories, including e.g. the
relativistic quantum-electrodynamics and the electron-fonon dynamics.


title: The Evolution and Revival Structure of Localized Quantum Wave Packets

abstract:
  Localized quantum wave packets can be produced in a variety of physical
systems and are the subject of much current research in atomic, molecular,
chemical, and condensed-matter physics. They are particularly well suited for
studying the classical limit of a quantum-mechanical system. The motion of a
localized quantum wave packet initially follows the corresponding classical
motion. However, in most cases the quantum wave packet spreads and undergoes a
series of collapses and revivals. We present a generic treatment of wave-packet
evolution, and we provide conditions under which various types of revivals
occur in ideal form. The discussion is at a level appropriate for an advanced
undergraduate or first-year graduate course in quantum mechanics. Explicit
examples of different types of revival structure are provided, and physical
applications are discussed.


title: Acceleration of Quantum Fields

abstract:
  We analyze the transformation of quantum fields under conformal coordinate
transformations from inertial to accelerated frames, in the simple case of
scalar massless fields in a two-dimensional spacetime, through the
transformation of particle number and its spectral density. Particle number is
found to be invariant under conformal coordinate transformations to uniformly
accelerated frames, which extends the property already known for vacuum.
Transformation of spectral density of particle number exhibits a redistribution
of particles in the frequency spectrum. This redistribution is determined by
derivatives of phase operators with respect to frequency, that is by time and
position operators defined in such a manner that the redistribution of
particles appears as a Doppler shift which depends on position in spacetime, in
conformity with Einstein equivalence principle.


title:
Classical behaviour in quantum mechanics: a transition probability
  approach

abstract:
  A formalism is developed for describing approximate classical behaviour in
finite (but possibly large) quantum systems. This is done in terms of a
structure common to classical and quantum mechanics, viz. a Poisson space with
a transition probability. Both the limit where Planck's constant goes to zero
in a fixed finite system and the limit where the size of the system goes to
infinity are incorporated. In either case, classical behaviour is seen only for
certain observables and in a restricted class of states.


title: Quantum Formalism with State-Collapse and Superluminal Communication

abstract:
  Given the collapse hypothesis (CH) of quantum measurement, EPR-type
correlations along with the hypothesis of the impossibility of superluminal
communication (ISC) have the effect of globalizing gross features of the
quantum formalism making them universally true. In particular, these hypotheses
imply that state transformations of density matrices must be linear and that
evolution which preserves purity of states must also be linear. A gedanken
experiment shows that lorentz covariance along with the second law of
thermodynamics imply a non-entropic version of ISC. Partial results using
quantum logic suggest, given ISC and a version of CH, a connection between
lorentz covariance and the covering law. These results show that standard
quantum mechanics is structurally unstable, and suggest that viable
relativistic alternatives must question CH. One may also speculate that some
features of the hilbert-space model of quantum mechanics have their origin in
space-time structure.


title: Quantum Error Correction by Coding

abstract:
  Recent progress in quantum cryptography and quantum computers has given hope
to their imminent practical realization. An essential element at the heart of
the application of these quantum systems is a quantum error correction scheme.
We propose a new technique based on the use of coding in order to detect and
correct errors due to imperfect transmission lines in quantum cryptography or
memories in quantum computers. We give a particular example of how to detect a
decohered qubit in order to transmit or preserve with high fidelity the
original qubit.


title:
General relation between state density and dwell times in mesoscopic
  systems

abstract:
  A relevant relation between the dwell time and the density of states for a
three dimensional system of arbitrary shape with an arbitrary number of
incoming channel is derived. This result extends the one obtained by Gasparian
et al. for the special case of a layered one dimensional symmetrical system. We
believe that such a strong relation between the most widely accepted time
related to the dynamics of a particle and the density of states in the barrier
region, one of the most relevant properties of a system in equilibrium, is rich
of physical significance.


title:
About Position Measurements Which Do Not Show the Bohmian Particle
  Position

abstract:
  ``Weak'', ``protective'', and ``delayed observation'' measurements are
analyzed in the framework of the Bohm interpretation of quantum theory. It is
argued that the above varieties of measurements manifest some difficulties of
the Bohm interpretation since they show that Bohmian trajectories behave not as
we would expect from a classical type model.


title: On Hegerfeldt's paradox

abstract:
  The acausal behavior of relativistic states exhibited by Hegerfeldt is shown
not to be present in physical systems described by first order in time
evolution equations.


title: Semiclassical Fourier Transform for Quantum Computation

abstract:
  Shor's algorithms for factorization and discrete logarithms on a quantum
computer employ Fourier transforms preceding a final measurement. It is shown
that such a Fourier transform can be carried out in a semi-classical way in
which a ``classical'' (macroscopic) signal resulting from the measurement of
one bit (embodied in a two-state quantum system) is employed to determine the
type of measurement carried out on the next bit, and so forth. In this way the
two-bit gates in the Fourier transform can all be replaced by a smaller number
of one-bit gates controlled by classical signals. Success in simplifying the
Fourier transform suggests that it may be worthwhile looking for other ways of
using semi-classical methods in quantum computing.


title: Measurement of conditional phase shifts for quantum logic

abstract:
  Measurements of the birefringence of a single atom strongly coupled to a
high-finesse optical resonator are reported, with nonlinear phase shifts
observed for intracavity photon number much less than one. A proposal to
utilize the measured conditional phase shifts for implementing quantum logic
via a quantum-phase gate (QPG) is considered. Within the context of a simple
model for the field transformation, the parameters of the "truth table" for the
QPG are determined.


title:
Pauli-Potential and Green Function Monte-Carlo Method for Many-Fermion
  Systems

abstract:
  The time evolution of a many-fermion system can be described by a Green's
function corresponding to an effective potential, which takes
anti-symmetrization of the wave function into account, called the
Pauli-potential. We show that this idea can be combined with the Green's
Function Monte Carlo method to accurately simulate a system of many
non-relativistic fermions. The method is illustrated by the example of systems
of several (2-9) fermions in a square well.


title: Noncommuting mixed states cannot be broadcast

abstract:
  We show that, given a general mixed state for a quantum system, there are no
physical means for {\it broadcasting\/} that state onto two separate quantum
systems, even when the state need only be reproduced marginally on the separate
systems. This result generalizes and extends the standard no-cloning theorem
for pure states.


title: On the Flux-Across-Surfaces Theorem

abstract:
  The quantum probability flux of a particle integrated over time and a distant
surface gives the probability for the particle crossing that surface at some
time. We prove the free Flux-Across-Surfaces Theorem, which was conjectured by
Combes, Newton and Shtokhamer, and which relates the integrated quantum flux to
the usual quantum mechanical formula for the cross section. The integrated
quantum flux is equal to the probability of outward crossings of surfaces by
Bohmian trajectories in the scattering regime.


title: Quantization of electromagnetic fields in a circular cylindrical cavity

abstract:
  We present a quantization procedure for the electromagnetic field in a
circular cylindrical cavity with perfectly conducting walls, which is based on
the decomposition of the field. A new decomposition procedure is proposed; all
vector mode functions satisfying the boundary conditions are obtained with the
help of this decomposition. After expanding the quantized field in terms of the
vector mode functions, it is possible to derive the Hamiltonian for this
quantized system.


title:
Group Theoretical Approach to the Coherent and the Squeeze States of a
  Time-Dependent Harmonic Oscillator with a Singular Term

abstract:
  For a time-dependent harmonic oscillator with an inverse squared singular
term, we find the generalized invariant using the Lie algebra of $SU(2)$ and
construct the number-type eigenstates and the coherent states using the
spectrum-generating Lie algebra of $SU(1,1)$. We obtain the evolution operator
in both of the Lie algebras. The number-type eigenstates and the coherent
states are constructed group-theoretically for both the time-independent and
the time-dependent harmonic oscillators with the singular term. It is shown
that the squeeze operator transforms unitarily the time-dependent basis of the
spectrum-generating Lie algebra of $SU(1,1)$ for the generalized invariant, and
thereby evolves the initial vacuum into a final coherent vacuum.


title: Coupling ``Classical'' and Quantum Variables

abstract:
  Experimentally, certain degrees of freedom may appear classical because their
quantum fluctuations are smaller than the experimental error associated with
measuring them. An approximation to a fully quantum theory is described in
which the self-interference of such ``quasiclassical'' variables is neglected
so that they behave classically when not coupled to other quantum variables.
Coupling to quantum variables can lead to evolution in which quasiclassical
variables do not have definite values, but values which are correlated to the
state of the quantum variables. A mathematical description implementing this
backreaction of the quantum variables on the quasiclassical variables is
critically discussed.


title: Spontaneous dissipation from generalized radiative corrections

abstract:
  We derive dissipative effective Hamiltonian for the unstable Lee model
without any ad hoc coarse graining procedure. Generalized radiative
corrections, utilizing the in-in formalism of quantum field theory,
automatically yield irreversibility as well as the decay of quantum coherence.
Especially we do not need to extend the ordinary Hilbert space for describing
the intrinsically dissipative system if we use the generalized in-in formalism
of quantum field theory.


title: Bohmian Mechanics as the Foundation of Quantum Mechanics

abstract:
  In order to arrive at Bohmian mechanics from standard nonrelativistic quantum
mechanics one need do almost nothing! One need only complete the usual quantum
description in what is really the most obvious way: by simply including the
positions of the particles of a quantum system as part of the state description
of that system, allowing these positions to evolve in the most natural way. The
entire quantum formalism, including the uncertainty principle and quantum
randomness, emerges from an analysis of this evolution. This can be expressed
succinctly---though in fact not succinctly enough---by declaring that the
essential innovation of Bohmian mechanics is the insight that {\it particles
move }!


title: Quantum state measurement by realistic heterodyne detection

abstract:
  The determination of the quantum properties of a single mode radiation field
by heterodyne or double homodyne detection is studied. The realistic case of
not fully efficient photodetectors is considered. It is shown that a large
amount of quite {\em precise} information is avalaible whereas the completeness
of such information is also discussed. Some examples are given and the special
case of states expressed as a finite superposition of number states is
considered in some detail.


title: Quantum Networks for Elementary Arithmetic Operations

abstract:
  Quantum computers require quantum arithmetic. We provide an explicit
construction of quantum networks effecting basic arithmetic operations: from
addition to modular exponentiation. Quantum modular exponentiation seems to be
the most difficult (time and space consuming) part of Shor's quantum
factorising algorithm. We show that the auxiliary memory required to perform
this operation in a reversible way grows linearly with the size of the number
to be factorised.


title: Quantum sources and a quantum coding theorem

abstract:
  We define a large class of quantum sources and prove a quantum analog of the
asymptotic equipartition property. Our proof relies on using local measurements
on the quantum source to obtain an associated classical source. The classical
source provides an upper bound for the dimension of the relevant subspace of
the quantum source, via the Shannon-McMillan noiseless coding theorem. Along
the way we derive a bound for the von Neumann entropy of the quantum source in
terms of the Shannon entropy of the classical source, and we provide a
definition of ergodicity of the quantum source. Several explicit models of
quantum sources are also presented.


title:
Quantum Equivalence Principle for Path Integrals in Spaces with
  Curvature and Torsion

abstract:
  We formulate a new quantum equivalence principle by which a path integral for
a particle in a general metric-affine space is obtained from that in a flat
space by a non-holonomic coordinate transformation. The new path integral is
free of the ambiguities of earlier proposals and the ensuing Schr\"odinger
equation does not contain the often-found but physically false terms
proportional to the scalar curvature. There is no more quantum ordering
problem. For a particle on the surface of a sphere in $D$ dimensions, the new
path integral gives the correct energy $\propto \hat L^2$ where $\hat L$ are
the generators of the rotation group in ${\bf x}$-space. For the transformation
of the Coulomb path integral to a harmonic oscillator, which passes at an
intermediate stage a space with torsion, the new path integral renders the
correct energy spectrum with no unwanted time-slicing corrections.


title: Born--Infeld theory of Electroweak and Gravitational fields

abstract:
  This paper has been withdrawn due to submission of subsequent versions as a
new preprint


title:
The von Neumann-Wigner type potentials and the wave functions'
  asymptotics for the discrete levels in continuum

abstract:
  One to one correspondence between the decay law of the von Neumann-Wigner
type potentials and the asymptotic behaviour of the wave functions representing
bound states in the continuum is established.


title: Localisation and Nonlocality in Compound Energy-Momentum Eigenstates

abstract:
  A thought experiment considering conservation of energy and momentum for a
pair of free bodies together with their internal energy is used to show the
existence of states that have localised position while being eigenstates of
energy and momentum. These states are applicable to all varieties of physical
bodies, including planets and stars in free motion in the universe. The states
are compound entanglements of multiple free bodies in which the momenta of the
bodies are anticorrelated so that they always sum to zero, while their total
kinetic energy is anticorrelated with their internal energies, so the total is
a constant, E. The bodies are relatively localised while the total state has
well-defined energy and momentum. These states do not violate Heisenberg
uncertainty because the total centre of mass is not localised, hence the states
naturally describe whole universes rather than isolated systems within a
universe. A further property of these states, resulting from the form of the
entanglement, is that they display nonlocality in the full sense of signal
transmission rather than the more restricted Bell sense.


title: The accelerated observer and quantum effects

abstract:
  An extended monopole detector at constant acceleration coupled to a massless
scalar field is allowed to evolve quantum mechanically. It is found that while
in the classical, followed by the point particle, limit the usual result Unruh
effect is recovered, in the point particle (before the classical) limit the
detector decouples from the scalar field and therefore the effect disappears.


title: Quantum Cryptography in Noisy Channels

abstract:
  We provide a complete proof of the security of quantum cryptography against
any eavesdropping attack including coherent measurements even in the presence
of noise. Polarization-based cryptographic schemes are shown to be equivalent
to EPR-based schemes. We also show that the performance of a noisy channel
approaches that of a noiseless one as the error rate tends to zero. (i.e., the
secrecy capacity $C_s (\epsilon) \to C_s (0)$ as $\epsilon \to 0$.) One
implication of our results is that one can {\it double} the efficiency of a
most well-known quantum cryptographic scheme proposed by Bennett and Brassard
simply by assigning vastly different probabilities to the two conjugate bases.


title: Quantum measurements and the Abelian Stabilizer Problem

abstract:
  We present a polynomial quantum algorithm for the Abelian stabilizer problem
which includes both factoring and the discrete logarithm. Thus we extend famous
Shor's results. Our method is based on a procedure for measuring an eigenvalue
of a unitary operator. Another application of this procedure is a polynomial
quantum Fourier transform algorithm for an arbitrary finite Abelian group. The
paper also contains a rather detailed introduction to the theory of quantum
computation.


title:
Purification of Noisy Entanglement and Faithful Teleportation via Noisy
  Channels

abstract:
  Two separated observers, by applying local operations to a supply of
not-too-impure entangled states ({\em e.g.} singlets shared through a noisy
channel), can prepare a smaller number of entangled pairs of arbitrarily high
purity ({\em e.g.} near-perfect singlets). These can then be used to faithfully
teleport unknown quantum states from one observer to the other, thereby
achieving faithful transfrom one observer to the other, thereby achieving
faithful transmission of quantum information through a noisy channel. We give
upper and lower bounds on the yield $D(M)$ of pure singlets ($\ket{\Psi^-}$)
distillable from mixed states $M$, showing $D(M)>0$ if
$\bra{\Psi^-}M\ket{\Psi^-}>\half$.


title: Quantum Mechanics as a Classical Theory VIII: Second Quantization

abstract:
  We continue in this paper our program of rederiving all quantum mechanical
formalism from the classical one. We now turn our attention to the derivation
of the second quantized equations, both for integral and half-integral spins.
We then show that all the quantum results may be derived using our approach and
also show the interpretation suggested by this derivation. This paper may be
considered as a first approach to the study of the quantum field theory
beginning by the same classical ideas we are supporting since the first paper
of this series.


title: Chance, Choice, and Consciousness: The Role of Mind in the Quantum Brain

abstract:
  Contemporary quantum mechanical description of nature involves two processes.
The first is a dynamical process governed by the equations of local quantum
field theory. This process is local and deterministic, but it generates a
structure that is not compatible with observed reality. A second process is
therefore invoked. This second process somehow analyzes the structure generated
by the first process into a collection of possible observable realities, and
selects one of these as the actually appearing reality. This selection process
is not well understood. It is necessarily nonlocal and, according to orthodox
thinking, is governed by an irreducible element of chance. The occurrence of
this irreducible element of chance means that the theory is not naturalistic:
the dynamics is controlled in part by something that is not part of the
physical universe. The present work describes a quantum mechanical model of
brain dynamics in which the quantum selection process is a causal process
governed not by pure chance but rather by a mathematically specified nonlocal
physical process identifiable as the conscious process.


title: Concentrating Partial Entanglement by Local Operations

abstract:
  If two separated observers are supplied with entanglement, in the form of $n$
pairs of particles in identical partly-entangled pure states, one member of
each pair being given to each observer; they can, by local actions of each
observer, concentrate this entanglement into a smaller number of
maximally-entangled pairs of particles, for example Einstein-Podolsky-Rosen
singlets, similarly shared between the two observers. The concentration process
asymptotically conserves {\em entropy of entanglement}---the von Neumann
entropy of the partial density matrix seen by either observer---with the yield
of singlets approaching, for large $n$, the base-2 entropy of entanglement of
the initial partly-entangled pure state. Conversely, any pure or mixed
entangled state of two systems can be produced by two classically-communicating
separated observers, drawing on a supply of singlets as their sole source of
entanglement.


title:
Quantum Electrodynamics at Large Distances II: Nature of the Dominant
  Singularities

abstract:
  Accurate calculations of macroscopic and mesoscopic properties in quantum
electrodynamics require careful treatment of infrared divergences: standard
treatments introduce spurious large-distances effects. A method for computing
these properties was developed in a companion paper. That method depends upon a
result obtained here about the nature of the singularities that produce the
dominant large-distance behaviour. If all particles in a quantum field theory
have non-zero mass then the Landau-Nakanishi diagrams give strong conditions on
the singularities of the scattering functions. These conditions are severely
weakened in quantum electrodynamics by effects of points where photon momenta
vanish. A new kind of Landau-Nakanishi diagram is developed here. It is geared
specifically to the pole-decomposition functions that dominate the macroscopic
behaviour in quantum electrodynamics, and leads to strong results for these
functions at points where photon momenta vanish.


title: Remarks on Consistent Histories and Bohmian Mechanics

abstract:
  Recent work with Dowker on the scientific status of the consistent histories
approach to quantum theory is reviewed and summarised. The approach is compared
with formulations of quantum theory, such as Bohmian mechanics and the
Copenhagen interpretation a la Landau-Lifshitz, in which classical variables
are explicitly appended. I try to explain why the consistent histories
formulation is scientifically problematic, in that it is a very weak theory,
but also scientifically interesting, shedding new light on quantum theory.


title: Coherent States for the Hydrogen Atom

abstract:
  The long-standing problem of finding coherent states for the (bound state
portion of the) hydrogen atom is positively resolved. The states in question:
(i) are normalized and are parameterized continuously, (ii) admit a resolution
of unity with a positive measure, and (iii) enjoy the property that the
temporal evolution of any coherent state by the hydrogen atom Hamiltonian
remains a coherent state for all time.


title:
Causal Wave Mechanics and the Advent of Complexity. I. Dynamic
  multivaluedness

abstract:
  Two major deviations from causality in the existing formulations of quantum
mechanics, related respectively to quantum chaos and indeterminate wave
reduction, are eliminated within the new, universal concept of dynamic
complexity. The analysis involves a new paradigm for description of a system
with interaction, the principle of dynamic multivaluedness (redundance), and
the ensuing concept of the fundamental dynamic uncertainty. It is shown that
both the wave reduction and truly unpredictable (chaotic) behaviour in quantum
systems can be completely and causally understood as a higher sublevel of the
same dynamic complexity that provides the causally complete picture of the
unified wave-particle duality and relativity at its lowest level
(quant-ph/9902015,16). The presentation is divided into five parts. The first
three parts deal with intrinsic randomness in Hamiltonian (isolated) quantum
systems as the basic case of dynamical chaos. In the last two parts a causal
solution to the problem of quantum indeterminacy and wave reduction is
proposed. Part I introduces the method of effective dynamical functions as a
generalisation of the optical potential formalism. The method provides a legal
transformation of the Schroedinger equation revealing the hidden
multivaluedness of interaction process, i. e. its self-consistent, dynamical
splitting into many equally real, but mutually incompatible branches, called
'realisations'. Each realisation incorporates the usual "complete" set of
eigenfunctions and eigenvalues for the entire problem. The method is presented
in detail for the Hamiltonian system with periodic (not small) perturbation,
both in its time-independent and time-dependent versions.


title:
Causal Wave Mechanics and the Advent of Complexity. II. Dynamic
  uncertainty in quantum systems and the correspondence principle

abstract:
  The intrinsic multivaluedness of interaction process, revealed in Part I of
this series of papers, is interpreted as the origin of the true dynamical (in
particular, quantum) chaos. The latter is causally deduced as unceasing series
of transitions, dynamically probabilistic by their origin, between the equally
real, but incompatible 'realisations' (modes of interaction) of a system. The
obtained set of realisations form the causally derived, intrinsically complete
"space of events" providing the crucial extension of the notion of probability
and the method of its first-principle calculation. The fundamental dynamic
uncertainty thus revealed is specified for Hamiltonian quantum systems and
applied to quantum chaos description in periodically perturbed systems. The
ordinary semiclassical transition in our quantum-mechanical results leads to
exact reproduction of the main features of chaotic behaviour of the system
known from classical mechanics, which permits one to "re-establish" the
correspondence principle for chaotic systems (inevitably lost in any their
conventional, single-valued description). The causal dynamical randomness in
the extended quantum mechanics is not restricted, however, to semiclassical
conditions and generically occurs also in essentially quantum regimes, even
though partial "quantum suppression of chaos" does exist and is specified in
our description, as well as other particular types of the quantum (truly)
chaotic behaviour.


title:
Causal Wave Mechanics and the Advent of Complexity. III. Universal
  structure of complexity

abstract:
  The universal dynamic uncertainty, discovered in Parts I and II of this
series of papers for the case of Hamiltonian quantum systems, is further
specified to reveal the hierarchical structure of levels of dynamically
redundant 'realisations' which takes the form of the intrinsically
probabilistic 'fundamental dynamical fractal' of a problem and determines
fractal character of the observed quantities. This intrinsic fractality is
obtained as a natural, causally derived property of dynamic behaviour of a
system with interaction and the corresponding complete solution. Every branch
of the fundamental dynamical fractal of a problem, as well as the probability
of its emergence, can be obtained within the extended nonperturbative analysis
of the main dynamic equation (Schroedinger equation in our case), contrary to
basically restricted imitations of fractality within the canonical,
single-valued approach. The results of the dynamical chaos analysis in
Hamiltonian quantum systems, Parts I-III, are then subjected to discussion and
generalisation. The physical origins of the dynamic uncertainty are analysed
from various points of view. The basic consequences, involving essential
extension of the conventional, unitary (= single-valued) quantum mechanics, are
summarised. Finally, we emphasize the universal character of the emerging
notions of dynamic multivaluedness (or redundance), causal randomness (or
dynamic uncertainty), first-principle probability, (non)integrability, general
solution, and physical complexity applicable to real dynamical systems of any
kind.


title:
Causal Wave Mechanics and the Advent of Complexity. IV. Dynamical origin
  of quantum indeterminacy and wave reduction

abstract:
  The concept of fundamental dynamic uncertainty (multivaluedness) developed in
Parts I-III of this work and used to establish the consistent understanding of
genuine chaos in Hamiltonian systems provides also causal description of the
quantum measurement process. The modified Schroedinger formalism involving
multivalued effective dynamical functions reveals the dynamic origin of quantum
measurement indeterminacy as the intrinsic instability in the compound system
of 'measured object' and (dissipative) 'instrument' with respect to splitting
into spatially localised 'realisations'. As a result, the originally wide
measured wave catastrophically (and really!) "shrinks" around a random
accessible point thus losing all its 'nonlocal properties' with respect to
other points/realisations. The dissipativity of one of the interacting objects
(serving as 'instrument') is reduced to its (arbitrarily small) openness
towards other systems (levels of complexity) and determines the difference
between quantum measurement and quantum chaos, the latter corresponding to an
effectively isolated system of interacting (micro-) objects. We do not use any
assumptions on particular "classical", "macroscopic", "stochastic", etc. nature
of the instrument or environment: physical reduction and indeterminacy
dynamically appear already in interaction between two microscopic (quantum)
deterministic systems, the object and the instrument, possessing just a few
degrees of freedom a part of which, belonging to the instrument, should
correspond to locally starting, arbitrarily weak excitation. This dynamically
indeterminate wave reduction occurs in agreement with the postulates of the
conventional quantum mechanics, including the rule of probabilities, which
transforms them into consequences of the dynamic uncertainty.


title:
Causal Wave Mechanics and the Advent of Complexity. V. Quantum field
  mechanics

abstract:
  The physical consequences of the analysis performed in Parts I-IV are
outlined within a scheme of the complete quantum (wave) mechanics called
quantum field mechanics and completing the original ideas of Louis de Broglie
by the dynamic complexity concept. The total picture includes the formally
complete description at the level of the "average" wave function of
Schroedinger type that shows dynamically chaotic behaviour in the form of
either quantum chaos (Parts I-III), or quantum measurement (Part IV) with
causal indeterminacy and wave reduction. This level is only an approximation,
though often sufficient, to a lower (and actually the lowest accessible) level
of complexity containing the causally complete version of the unreduced,
nonlinear "double solution" proposed by Louis de Broglie. The extended 'double
solution with chaos' describes the state of a nonlinear material field and
includes the unstable high-intensity "hump" moving chaotically within the
embedding smooth wave (quant-ph/9902015,16). The involvement of chaos causally
understood within the same concept of dynamic complexity (multivaluedness)
provides, at this lower level, de Broglie's "hidden thermodynamics" now,
however, without the necessity for any real "hidden thermostat". The chaotic
reduction of the "piloting" Schroedinger wave, at the higher sublevel of
complexity, conforms with the detailed 'wandering' of the virtual soliton at
the lower sublevel. The proposed dynamic multivaluedness (redundance) paradigm
serves as the basis for a self-consistent hierarchic picture of the world with
a (high) non-zero complexity (and thus irreducible randomness), where the
complete extension of quantum mechanics is causally interpreted as several
lowest levels of complexity.