title:
Self-cooling of a movable mirror to the ground state using radiation
  pressure

abstract:
  We show that one can cool a micro-mechanical oscillator to its quantum ground
state using radiation pressure in an appropriately detuned cavity
(self-cooling). From a simple theory based on Heisenberg-Langevin equations we
find that optimal self-cooling occurs in the good cavity regime, when the
cavity bandwidth is smaller than the mechanical frequency, but still larger
than the effective mechanical damping. In this case the intracavity field and
the vibrational mechanical mode coherently exchange their fluctuations. We also
present dynamical calculations which show how to access the mirror final
temperature from the fluctuations of the field reflected by the cavity.


title: Proper actions of lamplighter groups associated with free groups

abstract:
  Given a finite group $H$ and a free group $F_n$, we prove that the wreath
product $H\wr F_n$ admits a metrically proper, isometric action on a Hilbert
space.


title: Direct photons at LHC

abstract:
  The DGLAP improved color dipole approach provides a good description of data
for inclusive direct photon spectra at the energies of RHIC and Tevatron.
Within the same framework we predict the transverse momentum distribution of
direct photons at the CERN LHC energies.


title: Localization in a quasiperiodic model on quantum graphs

abstract:
  We show the presence of a dense pure point spectrum on quantum graphs with
Maryland-type quasiperiodic Kirchhoff coupling constants at the vertices.


title:
A distributed Approach for Access and Visibility Task under Ergonomic
  Constraints with a Manikin in a Virtual Reality Environment

abstract:
  This paper presents a new method, based on a multi-agent system and on
digital mock-up technology, to assess an efficient path planner for a manikin
for access and visibility task under ergonomic constraints. In order to solve
this problem, the human operator is integrated in the process optimization to
contribute to a global perception of the environment. This operator cooperates,
in real-time, with several automatic local elementary agents. The result of
this work validates solutions brought by digital mock-up and that can be
applied to simulate maintenance task.


title:
Coulomb potential in one dimension with minimal length: A path integral
  approach

abstract:
  We solve the path integral in momentum space for a particle in the field of
the Coulomb potential in one dimension in the framework of quantum mechanics
with the minimal length given by
  $(\Delta X)_{0}=\hbar \sqrt{\beta}$, where $\beta$ is a small positive
parameter. From the spectral decomposition of the fixed energy transition
amplitude we obtain the exact energy eigenvalues and momentum space
eigenfunctions.


title:
Dielectric relaxation and polar phonon softening in relaxor
  ferroelectric PbMg_(1/3)Ta_(2/3)O_3

abstract:
  Relaxor ferroelectric PbMg_1/3Ta_2/3O_3 ceramics and thin films were
investigated by means of broad-band dielectric, time-domain terahertz (THz) and
Fourier-transform infrared (IR) spectroscopy in the frequency range 100 Hz - 90
THz at temperatures 100 - 490 K, the THz and IR spectra were studied from 20 to
900K. Diffused and strongly temperature dependent peak in the complex
permittivity is caused by a dielectric relaxation due to the dynamics of polar
clusters. The relaxation appears below Burns temperature T_d in the THz range,
slows down on cooling through the microwave and MHz range and anomalously
broadens. The shortest and longest relaxation times of the distribution of
relaxation times follow Arrhenius and Vogel-Fulcher law, respectively. The
degree of B-site order has only a small influence on the parameters of the
dielectric relaxation and almost no influence on the phonon parameters. Below
T_m ~ 180K, the distribution of relaxation frequencies becomes broader than our
experimental spectral range and frequency independent dielectric losses develop
below 100 GHz in the spectra. Although the macroscopic crystal structure is
cubic, IR spectra give evidence about the lower local symmetry which can be
assigned to the presence of polar clusters below T_d. Infrared spectra above
T_d still reveal more modes than predicted by selection rules in the
paraelectric phase of the Fm-3m space group so that we suggest selection rules
which take into account chemical inhomogeneity in the beta''-perovskite
sublattice.


title: Neutrino mixings and magnetic moments due to Planck scale effects

abstract:
  In this paper, we consider the effect of Planck scale operators on neutrino
magnetic moments. We assume that the main part of neutrino masses and mixings
arise through GUT scale operators. We further assume that additional discrete
symmetries make the neutrino mixing bi-maximal. Quantum gravitational (Planck
scale) effects lead to an effective $SU(2)_{L}\times U(1)$ invariant
dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to
additional terms in neutrino mass matrix. These additional terms can be
considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix.
We assume that the gravitational interaction is flavour blind and we study the
neutrino mixings and magnetic moments due to the physics above the GUT scale.


title:
Evading 1/m_b-suppressed IR divergencies in QCDF: Bs-->KK Decays and
  B_{d,s} mixing

abstract:
  We analyze the deviations of the mixing induced CP asymmetry in B-->phi Ks
from sin(2beta), as well as the deviations of the asymmetries in Bs-->K*K*,
Bs-->phi K* and Bs-->phi phi from sin(2beta_s), that arise in SM due to penguin
pollution. We use a theoretical input which is short-distance dominated in
QCD-factorization and thus free of IR-divergencies. We also provide alternative
ways to extract angles of the unitarity triangle from penguin-mediated decays,
and give predictions for Bs-->K*K* observables.


title:
Structural plasticity of single chromatin fibers revealed by torsional
  manipulation

abstract:
  Magnetic tweezers are used to study the mechanical response under torsion of
single nucleosome arrays reconstituted on tandem repeats of 5S positioning
sequences. Regular arrays are extremely resilient and can reversibly
accommodate a large amount of supercoiling without much change in length. This
behavior is quantitatively described by a molecular model of the chromatin 3-D
architecture. In this model, we assume the existence of a dynamic equilibrium
between three conformations of the nucleosome, which are determined by the
crossing status of the entry/exit DNAs (positive, null or negative). Torsional
strain, in displacing that equilibrium, extensively reorganizes the fiber
architecture. The model explains a number of long-standing topological
questions regarding DNA in chromatin, and may provide the ground to better
understand the dynamic binding of most chromatin-associated proteins.


title: Generalised Fourier transform for the Camassa-Holm hierarchy

abstract:
  The squared eigenfunctions of the spectral problem associated to the
Camassa-Holm equation represent a complete basis of functions, which helps to
describe the Inverse Scattering Transform for the Camassa-Holm hierarchy as a
Generalised Fourier transform. The main result of this work is the derivation
of the completeness relation for the squared solutions of the Camassa-Holm
spectral problem. We show that all the fundamental properties of the
Camassa-Holm equation such as the integrals of motion, the description of the
equations of the whole hierarchy and their Hamiltonian structures can be
naturally expressed making use of the completeness relation and the recursion
operator, whose eigenfunctions are the squared solutions.


title:
Bridging the gap between stellar-mass black holes and ultraluminous
  X-ray sources

abstract:
  The X-ray spectral and timing properties of ultraluminous X-ray sources
(ULXs) have many similarities with the very high state of stellar-mass black
holes (power-law dominated, at accretion rates greater than the Eddington
rate). On the other hand, their cool disk components, large characteristic
inner-disk radii and low characteristic timescales have been interpreted as
evidence of black hole masses ~ 1000 Msun (intermediate-mass black holes). Here
we re-examine the physical interpretation of the cool disk model, in the
context of accretion states of stellar-mass black holes. In particular, XTE
J1550-564 can be considered the missing link between ULXs and stellar-mass
black holes, because it exhibits a high-accretion-rate, low-disk-temperature
state (ultraluminous branch). On the ultraluminous branch, the accretion rate
is positively correlated with the disk truncation radius and the bolometric
disk luminosity, while it is anti-correlated with the peak temperature and the
frequency of quasi-periodic-oscillations. Two prototypical ULXs (NGC1313 X-1
and X-2) also seem to move along that branch. We use a phenomenological model
to show how the different range of spectral and timing parameters found in the
two classes of accreting black holes depends on both their masses and accretion
rates. We suggest that ULXs are consistent with black hole masses ~ 50-100
Msun, moderately inefficiently accreting at ~20 times Eddington.


title:
A GIT Construction of Moduli Spaces of Stable Maps in Positive
  Characteristic

abstract:
  In a previous paper, the author and David Swinarski constructed the moduli
spaces of stable maps, \bar M_g,n(P^r,d), via geometric invariant theory (GIT).
That paper required the base field to be the complex numbers, a restriction
which this paper removes: here the coarse moduli spaces of stable maps are
constructed via GIT over a more general base.


title:
Quantum Auctions using Adiabatic Evolution: The Corrupt Auctioneer and
  Circuit Implementations

abstract:
  We examine a proposed auction using quantum states to represent bids and
distributed adiabatic search to find the winner. When the auctioneer follows
the protocol, the final measurement giving the outcome of the auction also
destroys the bid states, thereby preserving privacy of losing bidders. We
describe how a dishonest auctioneer could alter the protocol to violate this
privacy guarantee, and present methods by which bidders can counter such
attacks. We also suggest possible quantum circuit implementations of the
auctions protocol, and quantum circuits to perpetrate and to counter attacks by
a dishonest auctioneer.


title: The Mukai pairing, I: a categorical approach

abstract:
  We study the Hochschild homology of smooth spaces, emphasizing the importance
of a pairing which generalizes Mukai's pairing on the cohomology of K3
surfaces. We show that integral transforms between derived categories of spaces
induce, functorially, linear maps on homology. Adjoint functors induce adjoint
linear maps with respect to the Mukai pairing. We define a Chern character with
values in Hochschild homology, and we discuss analogues of the
Hirzebruch-Riemann-Roch theorem and the Cardy Condition from physics. This is
done in the context of a 2-category which has spaces as its objects and
integral kernels as its 1-morphisms.


title:
Variable X-ray Absorption toward Gravitationally-Lensed Blazar
  PKS1830-211

abstract:
  We present X-ray spectral analysis of five Chandra and XMM-Newton
observations of the gravitationally-lensed blazar PKS1830-211 from 2000 to
2004. We show that the X-ray absorption toward PKS1830-211 is variable, and the
variable absorption is most likely to be intrinsic with amplitudes of about
2-30e22 cm^-2 depending on whether or not the absorber is partially covering
the X-ray source. Our results confirm the variable absorption observed
previously, although interpreted differently, in a sequence of ASCA
observations. This large variation in the absorption column density can be
interpreted as outflows from the central engine in the polar direction,
consistent with recent numerical models of inflow/outflows in AGNs. In
addition, it could possibly be caused by the interaction between the blazar jet
and its environment, or the variation from the geometric configuration of the
jet. While the spectra can also be fitted with a variable absorption at the
lens redshift, we show that this model is unlikely. We also rule out the simple
microlensing interpretation of variability which was previously suggested.


title:
The structure of surfaces mapping to the moduli stack of canonically
  polarized varieties

abstract:
  Generalizing the well-known Shafarevich hyperbolicity conjecture, it has been
conjectured by Viehweg that a quasi-projective manifold that admits a
generically finite morphism to the moduli stack of canonically polarized
varieties is necessarily of log general type. Given a quasi-projective surface
that maps to the moduli stack, we employ extension properties of logarithmic
pluri-forms to establish a strong relationship between the moduli map and the
minimal model program of the surface. As a result, we can describe the
fibration induced by the moduli map quite explicitly. A refined affirmative
answer to Viehweg's conjecture for families over surfaces follows as a
corollary.


title: Confirmation of the 62 Day X-Ray Periodicity from M82

abstract:
  Using 400 days of new X-ray monitoring of M82, we confirm the 62 day
periodicity previously reported. In the full data set spanning 1124 days, we
find a period of 62.0 +/- 0.3 days and a coherence, Q = 22.3, that is
consistent with a strictly periodic signal. We estimate that the probability of
chance occurrence of our observed signal is 6E-7. The light curve folded at
this period is roughly sinusoidal and has a peak to peak amplitude of (0.99 +/-
0.10) x 10^-11 erg cm^-2 s^-1. Confirmation of the periodicity strengthens our
previous suggestion that the 62 day modulation is due to orbital motion within
an X-ray binary.


title:
Integral formulas for a class of curvature PDE's and applications to
  isoperimetric inequalities and to symmetry problems

abstract:
  We prove integral formulas for closed hypersurfaces in C^{n+1}, which furnish
a relation between elementary symmetric functions in the eigenvalues of the
complex Hessian matrix of the defining function and the Levi curvatures of the
hypersurface. Then we follow the Reilly approach to prove an isoperimetric
inequality. As an application, we obtain the ``Soap Bubble Theorem'' for
star-shaped domains with positive and constant Levi curvatures bounding the
classical mean curvature from above.


title:
A waiting time problem arising from the study of multi-stage
  carcinogenesis

abstract:
  We consider the population genetics problem: how long does it take before
some member of the population has $m$ specified mutations? The case $m=2$ is
relevant to onset of cancer due to the inactivation of both copies of a tumor
suppressor gene. Models for larger $m$ are needed for colon cancer and other
diseases where a sequence of mutations leads to cells with uncontrolled growth.


title: Two path transport measurements on a triple quantum dot

abstract:
  We present an advanced lateral triple quantum dot made by local anodic
oxidation. Three dots are coupled in a starlike geometry with one lead attached
to each dot thus allowing for multiple path transport measurements with two
dots per path. In addition charge detection is implemented using a quantum
point contact. Both in charge measurements as well as in transport we observe
clear signatures of states from each dot. Resonances of two dots can be
established allowing for serial transport via the corresponding path. Quadruple
points with all three dots in resonance are prepared for different electron
numbers and analyzed concerning the interplay of the simultaneously measured
transport along both paths.


title: Suppression of H_2 Cooling in the Ultraviolet Background

abstract:
  The first luminous objects in the concordance cosmology form by molecular
hydrogen cooling in dark matter dominated halos of masses ~10^6 M_sun. We use
Eulerian adaptive mesh refinement simulations to demonstrate that in the
presence of a large soft ultraviolet radiation background, molecular hydrogen
is the dominant coolant. Even for very large radiation backgrounds, the halo
masses that cool and collapse are up to two orders of magnitude smaller than
the halos that cool via atomic hydrogen line cooling. The abundance of cooling
halos and the cosmic mass fraction contained within them depends exponentially
on this critical mass scale. Consequently, the majority of current models of
cosmological reionization, chemical evolution, supermassive black hole
formation, and galaxy formation underestimate the number of star forming
progenitors of a given system by orders of magnitude. At the highest redshifts,
this disagreement is largest. We also show that even in the absence of residual
electrons, collisional ionization in central shocks create a sufficient amount
of electrons to form molecular hydrogen and cool the gas in halos of virial
temperatures far below the atomic cooling limit.


title: Decoherence of a Single Qubit from Quantum Anomaly

abstract:
  We show via an explicit example that quantum anomalies can lead to
decoherence of a single quantum qubit through phase relaxation. The anomaly
causes the Hamiltonian to develop a non-self-adjoint piece due to the
non-invariance of the domain of the Hamiltonian under symmetry transformation.
The resulting decoherence originates completely from the dynamics of the system
itself and not, as usually considered, from interactions with the environment.


title:
AC Hopping Magnetotransport Across the Spin Flop Transition in Lightly
  Doped La_2CuO_4

abstract:
  The weak ferromagnetism present in insulating La_{2}CuO_4 at low doping leads
to a spin flop transition, and to transverse (interplane) hopping of holes in a
strong external magnetic field. This results in a dimensional crossover 2D
$\to$ 3D for the in-plane transport, which in turn leads to an increase of the
hole's localization length and increased conduction. We demonstrate
theoretically that as a consequence of this mechanism, a frequency-dependent
jump of the in-plane ac hopping conductivity occurs at the spin flop
transition. We predict the value and the frequency dependence of the jump.
Experimental studies of this effect would provide important confirmation of the
emerging understanding of lightly doped insulating La_{2-x}Sr_xCuO_4.


title:
A study of the neglected Galactic HII region NGC 2579 and its companion
  ESO 370-9

abstract:
  The Galactic HII region NGC 2579 has stayed undeservedly unexplored due to
identification problems which persisted until recently. Both NGC 2579 and its
companion ESO 370-9 have been misclassified as planetary or reflection nebula,
confused with each other and with other objects. Due to its high surface
brightness, high excitation, angular size of few arcminutes and relatively low
interstellar extinction, NGC 2579 is an ideal object for investigations in the
optical range. Located in the outer Galaxy, NGC 2579 is an excellent object for
studying the Galactic chemical abundance gradients. In this paper we present
the first comprehensive observational study on the nebular and stellar
properties of NGC 2579 and ESO 370-9, including the determination of electron
temperature, density structure, chemical composition, kinematics, distance, and
the identification and spectral classification of the ionizing stars, and
discuss the nature of ESO 370-9. Long slit spectrophotometric data in the
optical range were used to derive the nebular electron temperature, density and
chemical abundances and for the spectral classification of the ionizing star
candidates. Halpha and UBV CCD photometry was carried out to derive stellar
distances from spectroscopic parallax and to measure the ionizing photon flux.


title: A Cavity Experiment to Search for Hidden Sector Photons

abstract:
  We propose a cavity experiment to search for low mass extra U(1) gauge bosons
with gauge-kinetic mixing with the ordinary photon, so-called paraphotons. The
setup consists of two microwave cavities shielded from each other. In one
cavity, paraphotons are produced via photon-paraphoton oscillations. The
second, resonant, cavity is then driven by the paraphotons that permeate the
shielding and reconvert into photons. This setup resembles the classic ``light
shining through a wall'' setup. However, the high quality factors achievable
for microwave cavities and the good sensitivity of microwave detectors allow
for a projected sensitivity for photon-paraphoton mixing of the order of
\chi~10^{-12} to 10^{-8}, for paraphotons with masses in the \mu eV to meV
range -- exceeding the current laboratory- and astrophysics-based limits by
several orders of magnitude. Therefore, this experiment bears significant
discovery potential for hidden sector physics.


title:
Star Formation via the Little Guy: A Bayesian Study of Ultracool Dwarf
  Imaging Surveys for Companions

abstract:
  I have undertaken a comprehensive statistical investigation of the ultracool
dwarf companion distribution (spectral type M6 and later). Utilizing a Bayesian
algorithm, I tested models of the companion distribution against data from an
extensive set of space and ground-based imaging observations of nearby
ultracool dwarfs. My main conclusions are fivefold: 1) Confirm that the
concentration of high mass ratio ultracool binary systems is a fundamental
feature of the companion distribution, not an observational or selection bias;
2) Determine that the wide (>~20 AU) binary frequency can be no more the 1-2%;
3) Show that the decreasing binary frequency with later spectral types is a
real trend; 4) Demonstrate that a large population of currently undetected low
mass ratio systems are not consistent with the current data; 5) Find that the
population of spectroscopic binaries must be be at least 30% that of currently
known ultracool binaries. The best fit value for the overall M6 and later
binary frequency is ~20%-22%, of which only ~6% consists of currently
undetected companions with separations less than 1 AU. If this is correct, then
the upper limit of the ultracool binary population discovered to date is ~75%.
I find that the numerical simulation results of the ejection formation method
are inconsistent with the outcome of this analysis. However, dynamics do seem
to play an important role as simulations of small-N clusters and triple system
decays produce results similar to those of this work. The observational efforts
required to improve these constraints are shown to be primarily large
spectroscopic binary surveys and improved high-resolution imaging techniques.


title: Dynamics of polarization buildup by spin filtering

abstract:
  There has been much recent research into polarizing an antiproton beam,
instigated by the recent proposal from the PAX (Polarized Antiproton
eXperiment) project at GSI Darmstadt. It plans to polarize an antiproton beam
by repeated interaction with a polarized internal target in a storage ring. The
method of polarization by spin filtering requires many of the beam particles to
remain within the ring after scattering off the polarized internal target via
electromagnetic and hadronic interactions. We present and solve sets of
differential equations which describe the buildup of polarization by spin
filtering in many different scenarios of interest to projects planning to
produce high intensity polarized beams. These scenarios are: 1) spin filtering
of a fully stored beam, 2) spin filtering while the beam is being accumulated,
i.e. unpolarized particles are continuously being fed into the beam, 3) the
particle input rate is equal to the rate at which particles are being lost due
to scattering beyond ring acceptance angle, the beam intensity remaining
constant, 4) increasing the initial polarization of a stored beam by spin
filtering, 5) the input of particles into the beam is stopped after a certain
amount of time, but spin filtering continues. The rate of depolarization of a
stored polarized beam on passing through an electron cooler is also shown to be
negligible.


title: High p_T Top Quarks at the Large Hadron Collider

abstract:
  Many new physics models predict resonances with masses in the TeV range which
decay into a pair of top quarks. With its large cross section, t\bar t
production at the Large Hadron Collider (LHC) offers an excellent opportunity
to search for such particles. The identification of very energetic top quarks
is crucial in such an analysis. We consider in detail the t\bar t\to\ell^\pm\nu
b\bar bq\bar q' (\ell=e, \mu) final state for high p_T top quarks. In this
phase space region, two or more of the final state quarks can merge into a
single jet due to the large Lorentz boost of the parent top quark. As a result,
a large fraction of t\bar t\to\ell^\pm\nu b\bar bq\bar q' events with an
invariant mass in the TeV region contains less than four observable jets.
Requiring one or two tagged b-quarks, we calculate the W+jets, Wb+jets, Wb\bar
b+jets, Wbt, and single top plus jets backgrounds for these final states, and
identify cuts which help to suppress them. In particular, we discuss whether a
cut on the jet invariant mass may be useful in reducing the background in the
\ell\nu+2 jets channel. We also investigate how next-to-leading order QCD
corrections affect high p_T top quark production at the LHC. We find that the
\ell\nu+2 jets and \ell\nu+3 jets final states with one or two $b$-tags will
significantly improve the chances for discovering new heavy particles in the
t\bar t channel at the LHC.


title: On the mass of the neutron star in V395 Car/2S 0921-630

abstract:
  We report high-resolution optical spectroscopy of the low-mass X-ray binary
V395 Car/2S 0921-630 obtained with the MIKE echelle spectrograph on the
Magellan-Clay telescope. Our spectra are obtained near superior conjunction of
the mass donor star and we exploit the absorption lines originating from the
back-side of the K-type object to accurately derive its rotational velocity.
Using K0-K1 III templates, we find vsini=32.9 +/- 0.8 km/s. We show that the
choice of template star and the assumed limb darkening coefficient has little
impact on the derived rotational velocity. This value is a significant revision
downwards compared to previously published values. We derive new system
parameter constraints in the light of our much lower rotational velocity. We
find M_1=1.44 +/- 0.10 Msun, M_2=0.35 +/- 0.03 Msun, and q=0.24 +/- 0.02 where
the errors have been estimated through a Monte-Carlo simulation. A possible
remaining systematic effect is the fact that we may be over-estimating the
orbital velocity of the mass donor due to irradiation effects. However, any
correction for this effect will only reduce the compact object mass further,
down to a minimum mass of M_1=1.05 +/- 0.08 Msun. There is thus strong evidence
that the compact object in this binary is a neutron star of rather typical mass
and that the previously reported mass values of 2-4Msun were too high due to an
over-estimate of the rotational broadening.


title: Effective potentials for heavy quarks above deconfinement

abstract:
  Using methods previously developed by Kelbg and others for creating effective
potentials for electron-ion plasmas, we investigate quarkonium potentials above
deconfinement. Using results for the internal energy of a static
quark-antiquark pair, a set of effective potentials are constructed that take
into account quantum effects and symmetry conditions. Bound state effects are
explicitly included in order to account for the strongly coupled nature of
plasmas. It is hoped that these effective potentials will be useful in
simulations of heavy quarks or plasma quasiparticles when the dynamics is
treated classically.


title:
Constant Mean Curvature Hypersurfaces in the (n+1)-Sphere by Gluing
  Spherical Building Blocks

abstract:
  The techniques developed by Butscher in arXiv:math/0703469 for constructing
constant mean curvature (CMC) hypersurfaces in the (n+1)-sphere by gluing
together spherical building blocks are generalized to handle less symmetric
initial configurations. The outcome is that the approximately CMC hypersurface
obtained by gluing the initial configuration together can be perturbed into an
exactly CMC hypersurface only when certain global geometric conditions are met.
These `balancing conditions' are analogous to those that must be satisfied in
the `classical' context of gluing constructions of CMC hypersurfaces in
Euclidean space, although they are more restrictive in the (n+1)-sphere case.
An example of an initial configuration is given which demonstrates this fact;
and another example of an initial configuration is given which possesses no
symmetries at all.


title:
The cosmic 6Li and 7Li problems and BBN with long-lived charged massive
  particles

abstract:
  Charged massive particles (CHAMPs), when present during the Big Bang
nucleosynthesis (BBN) era, may significantly alter the synthesis of light
elements when compared to a standard BBN scenario. This is due to the formation
of bound states with nuclei. This paper presents a detailed numerical and
analytical analysis of such CHAMP BBN. All reactions important for predicting
light-element yields are calculated within the Born approximation. Three
priorly neglected effects are treated in detail:(a) photodestruction of bound
states due to electromagnetic cascades induced by the CHAMP decay, (b)
late-time efficient destruction/production of H2, Li6, and Li7 due to reactions
on charge Z=1 nuclei bound to CHAMPs, and (c) CHAMP exchange between nuclei.
Each of these effects may induce orders-of-magnitude changes in the final
abundance yields. The study focusses on the impact of CHAMPs on a possible
simultaneous solution of the Li6 and Li7 problems. It is shown that a priorly
suggested simultaneous solution of the Li6 and Li7 problems for a relic
decaying at tau_x = 1000 sec is only very weakly dependent on the relic being
neutral or charged, unless its hadronic branching ratio is Bh << 10^-4 very
small. By use of a Monte-Carlo analysis it is shown that within CHAMP BBN the
existence of further parameter space for a simultaneous solution of the Li6 and
Li7 problem for long decay times tau_x > 10^6 sec seems possible but fairly
unlikely.


title:
Symmetric Informationally-Complete Quantum States as Analogues to
  Orthonormal Bases and Minimum-Uncertainty States

abstract:
  Since Renes et al. [J. Math. Phys. 45, 2171 (2004)], there has been much
effort in the quantum information community to prove (or disprove) the
existence of symmetric informationally complete (SIC) sets of quantum states in
arbitrary finite dimension. This paper strengthens the urgency of this question
by showing that if SIC-sets exist: 1) by a natural measure of orthonormality,
they are as close to being an orthonormal basis for the space of density
operators as possible, and 2) in prime dimensions, the standard construction
for complete sets of mutually unbiased bases and Weyl-Heisenberg covariant
SIC-sets are intimately related: The latter represent minimum uncertainty
states for the former in the sense of Wootters and Sussman. Finally, we
contribute to the question of existence by conjecturing a quadratic redundancy
in the equations for Weyl-Heisenberg SIC-sets.


title:
Evidence for gapped spin-wave excitations in the frustrated Gd2Sn2O7
  pyrochlore antiferromagnet from low-temperature specific heat measurements

abstract:
  We have measured the low-temperature specific heat of the geometrically
frustrated pyrochlore Heisenberg antiferromagnet Gd2Sn2O7 in zero magnetic
field. The specific heat is found to drop exponentially below approximately 350
mK. This provides evidence for a gapped spin-wave spectrum due to an anisotropy
resulting from single ion effects and long-range dipolar interactions. The data
are well fitted by linear spin-wave theory, ruling out unconventional low
energy magnetic excitations in this system, and allowing a determination of the
pertinent exchange interactions in this material.


title:
Use of negative capacitance to provide a sub-threshold slope lower than
  60 mV/decade

abstract:
  It is well known that conventional Field Effect Transistors (FET's) require a
change in the channel potential of at least 60 mV at 300K to effect a change in
the current by a factor of ten, and this minimum subthreshold slope S puts a
lower limit of fundamental nature on the operating voltage and hence the power
dissipation in standard FET based switches. Here we show that by replacing the
standard insulator with a ferroelectric insulator of the right thickness it
should be possible to implement a step-up voltage transformer that will amplify
the gate voltage thus leading to values of S lower than 60 mV/decade and
enabling low voltage/low power operation. The voltage transformer action can be
understood intuitively as the result of an effective negative capacitance
provided by the ferroelectric capacitor which arises from an internal positive
feedback that in principle could be obtained from other microscopic mechanisms
as well. Unlike other proposals to reduce S this involves no change in the
basic physics of the FET and thus does not affect its current drive or impose
other restrictions.


title: Top off the unparticle

abstract:
  The existence of an exactly scale invariant sector possessing a non-trivial
infrared fixed point at a higher energy scale and its possible communication
with the Standard Model particles through a heavy messenger sector has been
shown to lead to curious unparticle effects. We demonstrate that top physics at
the Tevatron can already constrain such theories. We also consider possible
improvements at the LHC and delineate some striking signatures.


title: Fractalization drives crystalline states in a frustrated spin system

abstract:
  We measure a sequence of quantum Hall-like plateaux at 1/q: 9 >= q >= 2 and
p/q = 2/9 fractions in the magnetisation with increasing magnetic field in the
geometrically frustrated spin system SrCu2(BO3)2. We find that the entire
observed sequence of plateaux is reproduced by solving the Hofstadter problem
on the system lattice when short-range repulsive interactions are included,
thus providing a sterling demonstration of bosons confined by a magnetic and
lattice potential mimicking fermions in the extreme quantum limit.


title: Node similarity within subgraphs of protein interaction networks

abstract:
  We propose a biologically motivated quantity, twinness, to evaluate local
similarity between nodes in a network. The twinness of a pair of nodes is the
number of connected, labeled subgraphs of size n in which the two nodes possess
identical neighbours. The graph animal algorithm is used to estimate twinness
for each pair of nodes (for subgraph sizes n=4 to n=12) in four different
protein interaction networks (PINs). These include an Escherichia coli PIN and
three Saccharomyces cerevisiae PINs -- each obtained using state-of-the-art
high throughput methods. In almost all cases, the average twinness of node
pairs is vastly higher than expected from a null model obtained by switching
links. For all n, we observe a difference in the ratio of type A twins (which
are unlinked pairs) to type B twins (which are linked pairs) distinguishing the
prokaryote E. coli from the eukaryote S. cerevisiae. Interaction similarity is
expected due to gene duplication, and whole genome duplication paralogues in S.
cerevisiae have been reported to co-cluster into the same complexes. Indeed, we
find that these paralogous proteins are over-represented as twins compared to
pairs chosen at random. These results indicate that twinness can detect
ancestral relationships from currently available PIN data.


title:
Approximate zero-one laws and sharpness of the percolation transition in
  a class of models including 2D Ising percolation

abstract:
  One of the most well-known classical results for site percolation on the
square lattice is the equation p_c + p_c^* = 1. In words, this equation means
that for all values different from p_c of the parameter p the following holds:
Either a.s. there is an infinite open cluster or a.s. there is an infinite
closed `star' cluster. This result is closely related to the percolation
transition being sharp: Below p_c the size of the open cluster of a given
vertex is not only (a.s.) finite, but has a distrubtion with an exponential
tail. The analog of this result has been proved by Higuchi in 1993 for
two-dimensional Ising percolation, with fixed inverse temparature beta <beta_c,
and as parameter the external field h.
  Using sharp-threshold results (approximate zero-one laws) and a modification
of an RSW-like result by Bollobas and Riordan, we show that these results hold
for a large class of percolation models where the vertex values can be `nicely'
represented (in a sense which will be defined precisely) by i.i.d. random
variables. We point out that the ordinary percolation model belongs obviously
to this class, and we show that also the above mentionedIsing model belongs to
it.
  We hope that our results improve insight in the Ising percolation model, and
will help to show that many other (not yet analyzed) weakly dependent
percolation models also belong to the abovementioned class.


title:
Quantum transport of Dirac electrons in graphene in the presence of a
  spatially modulated magnetic field

abstract:
  We have investigated the electrical transport properties of Dirac electrons
in a monolayer graphene sheet in the presence of a perpendicular magnetic field
that is modulated weakly and periodically along one direction.We find that the
Landau levels broaden into bands and their width oscillates as a function of
the band index and the magnetic field.We determine the $\sigma_{yy}$ component
of the magnetoconductivity tensor for this system which is shown to exhibit
Weiss oscillations.We also determine analytically the asymptotic expressions
for $\sigma_{yy}$.We compare these results with recently obtained results for
electrically modulated graphene as well as those for magnetically modulated
conventional two-dimensional electron gas (2DEG) system.We find that in the
magnetically modulated graphene system cosidered in this work,Weiss
oscillations in $\sigma_{yy}$ have a reduced amplitude compared to the 2DEG but
are less damped by temperature while they have a higher amplitude than in the
electrically modulated graphene system. We also find that these oscillations
are out of phase by $\pi$ with those of the electrically modulated system while
they are in phase with those in the 2DEG system.


title: Nearly optimal embeddings of trees

abstract:
  In this paper we show how to find nearly optimal embeddings of large trees in
several natural classes of graphs. The size of the tree T can be as large as a
constant fraction of the size of the graph G, and the maximum degree of T can
be close to the minimum degree of G. For example, we prove that any graph of
minimum degree d without 4-cycles contains every tree of size \epsilon d^2 and
maximum degree at most (1-2\epsilon)d - 2. As there exist d-regular graphs
without 4-cycles of size O(d^2), this result is optimal up to constant factors.
We prove similar nearly tight results for graphs of given girth, graphs with no
complete bipartite subgraph K_{s,t}, random and certain pseudorandom graphs.
These results are obtained using a simple and very natural randomized embedding
algorithm, which can be viewed as a "self-avoiding tree-indexed random walk".


title:
UV Luminosity Functions at z~4, 5, and 6 from the HUDF and other Deep
  HST ACS Fields: Evolution and Star Formation History

abstract:
  We use the ACS BViz data from the HUDF and all other deep HST ACS fields
(including the GOODS fields) to find large samples of star-forming galaxies at
z~4 and z~5 and to extend our previous z~6 sample. These samples contain 4671,
1416, and 627 B, V, and i dropouts, respectively, and reach to extremely low
luminosities (0.01-0.04 L* or M(UV)~-16 to -17), allowing us to determine the
rest-frame UV luminosity function (LF) and faint-end slope alpha at z~4-6 to
high accuracy. We find faint-end slopes alpha of -1.73+/-0.05 at z~4,
-1.66+/-0.09 at z~5, and -1.74+/-0.16 at z~6 -- suggesting that the faint-end
slope is very steep and shows little evolution with cosmic time. We find that
M*(UV) brightens considerably in the 0.7 Gyr from z~6 to z~4 (by ~0.7 mag from
M*=-20.24+/-0.19 to M*=-20.98+/-0.10). The observed increase in the
characteristic luminosity over this range is almost identical to that expected
for the halo mass function -- suggesting that the observed evolution is likely
due to the hierarchical coalescence and merging of galaxies. The evolution in
phi* is not significant. The UV luminosity density at z~6 is modestly lower
(0.45+/-0.09 times) than that at z~4 (integrated to -17.5 AB mag) though a
larger change is seen in the dust-corrected star-formation rate density. We
thoroughly examine published LF results and assess the reasons for their wide
dispersion. We argue that the results reported here are the most robust
available. The extremely steep faint-end slopes alpha found here suggest that
lower luminosity galaxies play a significant role in reionizing the universe.
Finally, we consider recent search results for galaxies at z~7-8 and use them
to extend our estimates of the evolution in M* from z~7-8 to z~4.


title: No-Bang Quantum State of the Cosmos

abstract:
  A quantum state of the entire cosmos (universe or multiverse) is proposed
which is the equal mixture of the Giddings-Marolf states that are
asymptotically single de Sitter spacetimes in both past and future and are
regular on the throat or neck of minimal three-volume. That is, states are
excluded that have a big bang or big crunch or which split into multiple
asymptotic de Sitter spacetimes. (For simplicity, transitions between different
values of the cosmological constant are assumed not to occur, though different
positive values are allowed.) The entropy of this mixed state appears to be of
the order of the three-fourths power of the Bekenstein-Hawking A/4 entropy of
de Sitter spacetime. Most of the component pure states do not have rapid
inflation, but when an inflaton is present and the states are weighted by the
volume at the end of inflation, a much smaller number of states may dominate
and give a large amount of inflation and hence may agree with observations.


title: Factorized world-sheet scattering in near-flat AdS_5 x S^5

abstract:
  We show the factorization of the three-particle world-sheet S-matrix of AdS_5
x S^5 superstring theory in the near-flat-space limit at one loop order. This
is done by computing various scattering amplitudes from Feynman diagrams in the
world-sheet theory. The knowledge of certain highest weight amplitudes allows
us to fix all the freedom in the three-particle S-matrix, which we argue to be
constrained up to four scalar functions due to the symmetries of the model. We
demonstrate that these amplitudes are given by corresponding products of the
known two-particle S-matrix elements, from which it follows that the scattering
of any three world-sheet excitations factorizes. This provides an explicit and
direct check of the quantum integrability of string theory in near-flat AdS_5 x
S^5 as it renders evidence for the existence of higher conserved charges. By
computing further amplitudes we also obtain an indirect confirmation of the
supersymmetries of the near-flat-space model.


title:
Filling the holes: Evolving excised binary black hole initial data with
  puncture techniques

abstract:
  We follow the inspiral and merger of equal-mass black holes (BHs) by the
moving puncture technique and demonstrate that both the exterior solution and
the asymptotic gravitational waveforms are unchanged when the initial interior
solution is replaced by constraint-violating ``junk'' initial data. We apply
this result to evolve conformal thin-sandwich (CTS) binary BH initial data by
filling their excised interiors with arbitrary, but smooth, initial data and
evolving with standard puncture gauge choices. The waveforms generated for both
puncture and filled-CTS initial data are remarkably similar, and there are only
minor differences between irrotational and corotational CTS BH binaries. Even
the interior solutions appear to evolve to the same constraint-satisfying
solution at late times, independent of the initial data.


title: A quantum topological phase transition at the microscopic level

abstract:
  We study a quantum phase transition between a phase which is topologically
ordered and one which is not. We focus on a spin model, an extension of the
toric code, for which we obtain the exact ground state for all values of the
coupling constant that takes the system across the phase transition. We compute
the entanglement and the topological entropy of the system as a function of
this coupling constant, and show that the topological entropy remains constant
all the way up to the critical point, and jumps to zero beyond it. Despite the
jump in the topological entropy, the transition is second order as detected via
any local observable.


title:
Lagrangian embeddings of the Klein bottle and combinatorial properties
  of mapping class groups

abstract:
  A proof of non-existence of Lagrangian embeddings of the Klein bottle K in
\CP^2 is given. We exploit the existence of a special embedding of K in a
symplectic Lefschetz pencil on \CP^2 and study its monodromy. As the main
technical tool, we develop the theory of mapping class groups, considered as
quotients of special Artin braid groups, and obtain some new results about
combinatorial structure of such groups.


title: Cosmic Ray production of Beryllium and Boron at high redshift

abstract:
  Recently, new observations of Li6 in Pop II stars of the galactic halo have
shown a surprisingly high abundance of this isotope, about a thousand times
higher than its predicted primordial value. In previous papers, a cosmological
model for the cosmic ray-induced production of this isotope in the IGM has been
developed to explain the observed abundance at low metallicity. In this paper,
given this constraint on the Li6, we calculate the non-thermal evolution with
redshift of D, Be, and B in the IGM. In addition to cosmological cosmic ray
interactions in the IGM, we include additional processes driven by SN
explosions: neutrino spallation and a low energy component in the structures
ejected by outflows to the IGM. We take into account CNO CRs impinging on the
intergalactic gas. Although subdominant in the galactic disk, this process is
shown to produce the bulk of Be and B in the IGM, due to the differential metal
enrichment between structures (where CRs originate) and the IGM. We also
consider the resulting extragalactic gamma-ray background which we find to be
well below existing data. The computation is performed in the framework of
hierarchical structure formation considering several star formation histories
including Pop III stars. We find that D production is negligible and that a
potentially detectable Be and B plateau is produced by these processes at the
time of the formation of the Galaxy (z ~ 3).


title: Dynamics of Free Surface Perturbations Along an Annular Viscous Film

abstract:
  It is known that an axisymmetric viscous film flowing down the outside of a
thin vertical fiber becomes unstable to interfacial perturbations. We present
an experimental study using fluids with different densities, surface tensions
and viscosities to investigate the growth and dynamics of these interfacial
perturbations and to test the assumptions made by previous authors. We find the
initial perturbation growth is exponential followed by a slower phase as the
amplitude and wavelength saturate in size. Measurements of the perturbation
growth for experiments conducted at low and moderate Reynolds numbers are
compared to theoretical predictions developed from linear stability theory.
Excellent agreement is found between predictions from a long-wave Stokes flow
model (Craster & Matar, J. Fluid Mech. 553, 85 (2006)) and data, while fair
agreement is found between predictions from a moderate Reynolds number model
(Sisoev et al., Chem. Eng. Sci. 61, 7279 (2006)) and data. Furthermore, we find
that a known transition in the longer-time perturbation dynamics from unsteady
to steady behavior at a critical flow rate, Qc, is correlated to a transition
in the rate at which perturbations naturally form along the fiber. For Q < Qc
(steady case), the rate of perturbation formation is constant. As a result the
position along the fiber where perturbations form is nearly fixed, and the
spacing between consecutive perturbations remains constant as they travel 2 m
down the fiber. For Q > Qc (unsteady case), the rate of perturbation formation
is modulated. As a result the position along the fiber where perturbations form
oscillates irregularly, and the initial speed and spacing between perturbations
varies resulting in the coalescence of neighboring perturbations further down
the fiber.


title: Generalized gradient approximation for solids and their surfaces

abstract:
  Successful modern generalized gradient approximations (GGA) are biased toward
atomic energies. Restoration of the first-principles gradient expansion for the
exchange energy over a wide range of density gradients eliminates this bias. We
introduce PBEsol, a revised Perdew-Burke-Ernzerhof GGA that improves
equilibrium properties for many densely-packed solids and their surfaces.


title:
Exact models with non-minimal interaction between dark matter and
  (either phantom or quintessence) dark energy

abstract:
  A method for deriving Friedmann-Robertson-Walker (FRW) solutions developed in
Int. J. Mod. Phys. D{\bf 5}(1996)71-84, is generalized to account for models
with non-minimal coupling between the dark energy and the dark matter. New
quintessence and phantom (flat) FRW solutions are found. Their physical
significance is discussed. Additionally, the aforementioned method is modified
so that, "coincidence free" solutions can be readily derived. Besides, we
review some aspects of the phantom barrier crossing. In this regard we present
a model which is free from the coincidence problem and, at the same time, does
the crossing of the phantom barrier $\omega=-1$ at late time. Finally, we give
additional comments on the non predictive properties of scalar field
cosmological models with or without energy transfer.


title: A Training based Distributed Non-Coherent Space-Time Coding Strategy

abstract:
  Unitary space-time modulation is known to be an efficient means to
communicate over non-coherent Multiple Input Multiple Output (MIMO) channels.
In this letter, differential unitary space-time coding and non-coherent
space-time coding for the training based approach of Kim and Tarokh are
addressed. For this approach, necessary and sufficient conditions for
multi-group decodability are derived in a simple way assuming a Generalized
Likelihood Ratio Test receiver and a unitary codebook. Extending Kim and
Tarokh's approach for colocated MIMO systems, a novel training based approach
to distributed non-coherent space-time coding for wireless relay networks is
proposed. An explicit construction of two-group decodable distributed
non-coherent space-time codes achieving full cooperative diversity for all even
number of relays is provided.


title: Amine-Gold Linked Single-Molecule Junctions: Experiment and Theory

abstract:
  The measured conductance distribution for single molecule benzenediamine-gold
junctions, based on 59,000 individual conductance traces recorded while
breaking a gold point contact in solution, has a clear peak at 0.0064 G$_{0}$
with a width of $\pm$ 40%. Conductance calculations based on density functional
theory (DFT) for 15 distinct junction geometries show a similar spread.
Differences in local structure have a limited influence on conductance because
the amine-Au bonding motif is well-defined and flexible. The average calculated
conductance (0.046 G$_{0}$) is seven times larger than experiment, suggesting
the importance of many-electron corrections beyond DFT.


title:
Ellipses of minimal area and of minimal eccentricity circumscribed about
  a convex quadrilateral

abstract:
  First, we fill in key gaps in Steiner's nice characterization of the most
nearly circular ellipse which passes through the vertices of a convex
quadrilateral, D. Steiner proved that there is only one pair of conjugate
directions, M1 and M2, that belong to all ellipses of circumscription. Then he
proves that if there is an ellipse, E, whose equal conjugate diameters possess
the directional constants M1 and M2, then E must be an ellipse of
circumscription which has minimal eccentricity. However, Steiner does not show
the existence or uniqueness of such an ellipse. We prove that there is a unique
ellipse of minimal eccentricity which passes through the vertices of D. We also
show that there exists an ellipse which passes through the vertices of D and
whose equal conjugate diameters possess the directional constants M1 and M2. We
also show that there exists a unique ellipse of minimal area which passes
through the vertices of D. Finally, we call a convex quadrilateral, D,
bielliptic if the unique inscribed and circumscribed ellipses of minimal
eccentricity have the same eccentricity. This generalizes the notion of
bicentric quadrilaterals. In particular we show the existence of a bielliptic
convex quadrilateral which is not bicentric.


title:
X-ray and Near-IR Variability of the Anomalous X-ray Pulsar 1E
  1048.1-5937: From Quiescence Back to Activity

abstract:
  (Abridged) We report on new and archival X-ray and near-infrared observations
of the anomalous X-ray pulsar 1E 1048.1-5937 performed between 2001-2007 with
RXTE, CXO, Swift, HST, and VLT. During its ~2001-2004 active period, 1E
1048.-5937 exhibited two large, long-term X-ray pulsed-flux flares as well as
short bursts, and large (>10x) torque changes. Monitoring with RXTE revealed
that the source entered a phase of timing stability in 2004; at the same time,
a series of four simultaneous observations with CXO and HST in 2006 showed that
its X-ray flux and spectrum and near-IR flux, all variable prior to 2005,
stabilized. The near-IR flux, when detected by HST (H~22.7 mag) and VLT
(K_S~21.0 mag), was considerably fainter than previously measured. Recently, in
2007 March, this newfound quiescence was interrupted by a sudden flux
enhancement, X-ray spectral changes and a pulse morphology change, simultaneous
with a large spin-up glitch and near-IR enhancement. Our RXTE observations
revealed a sudden pulsed flux increase by a factor of ~3 in the 2-10 keV band.
In observations with CXO and Swift, we found that the total X-ray flux
increased much more than the pulsed flux, reaching a peak value of >7 times the
quiescent value (2-10 keV). With these recent data, we find a strong
anti-correlation between X-ray flux and pulsed fraction, and a correlation
between X-ray spectral hardness and flux. Simultaneously with the radiative and
timing changes, we observed a significant X-ray pulse morphology change such
that the profile went from nearly sinusoidal to having multiple peaks. We
compare these remarkable events with other AXP outbursts and discuss
implications in the context of the magnetar model and other models of AXP
emission.


title: Discovery of two new accreting pulsating white dwarf stars

abstract:
  We report the discovery of two new accreting pulsating white dwarf stars
amongst the cataclysmic variables of the Sloan Digital Sky Survey:
SDSSJ074531.91+453829.5 and SDSSJ091945.10+085710.0. We observe high amplitude
non-sinusoidal variations of 4.5-7% at a period close to 1230s in the optical
light curves of SDSSJ074531.91+453829.5 and a low amplitude variation of
0.7-1.6% near 260s in the light curves of SDSSJ091945.10+085710.0. We infer
that these optical variations are a consequence of nonradial g-mode pulsations
in the accreting primary white dwarfs of these cataclysmic variables. However
we cannot rule out the remote possibility that the 260s period could be the
spin period of the accreting white dwarf SDSSJ091945.10+085710.0. We also
uncovered a non-variable SDSSJ171145.08+301320.0 during our search; our two
observing runs exclude any pulsation related periodicities in the range of
85-1400s with an amplitude greater than or equal to 0.5%. This discovery paper
brings the total number of known accreting white dwarf pulsators to eleven.


title:
Universal nature of particle displacements close to glass and jamming
  transitions

abstract:
  We examine the structure of the distribution of single particle displacements
(van-Hove function) in a broad class of materials close to glass and jamming
transitions. In a wide time window comprising structural relaxation, van-Hove
functions reflect the coexistence of slow and fast particles (dynamic
heterogeneity). The tails of the distributions exhibit exponential, rather than
Gaussian, decay. We argue that this behavior is universal in glassy materials
and should be considered the analog, in space, of the stretched exponential
decay of time correlation functions. We introduce a dynamical model that
describes quantitatively numerical and experimental data in supercooled
liquids, colloidal hard spheres and granular materials. The tails of the
distributions directly explain the decoupling between translational diffusion
and structural relaxation observed in glassy materials.


title: Non-Markovian dynamics of a qubit coupled to an Ising spin bath

abstract:
  We study the analytically solvable Ising model of a single qubit system
coupled to a spin bath. The purpose of this study is to analyze and elucidate
the performance of Markovian and non-Markovian master equations describing the
dynamics of the system qubit, in comparison to the exact solution. We find that
the time-convolutionless master equation performs particularly well up to
fourth order in the system-bath coupling constant, in comparison to the
Nakajima-Zwanzig master equation. Markovian approaches fare poorly due to the
infinite bath correlation time in this model. A recently proposed
post-Markovian master equation performs comparably to the time-convolutionless
master equation for a properly chosen memory kernel, and outperforms all the
approximation methods considered here at long times. Our findings shed light on
the applicability of master equations to the description of reduced system
dynamics in the presence of spin-baths.


title:
Evolution of density perturbations in double exponential quintessence
  models

abstract:
  In this work we investigate the evolution of matter density perturbations for
quintessence models with a self-interaction potential that is a combination of
exponentials. One of the models is based on the Einstein theory of gravity,
while the other is based on the Brans-Dicke scalar tensor theory. We constrain
the parameter space of the models using the determinations for the growth rate
of perturbations derived from data of the 2-degree Field Galaxy Redshift
Survey.


title: Conjectures on Partitions of Integers as Summations of Primes

abstract:
  In this short note we present a class of conjectures on partitions of
integers as summations of primes, which are extensions of Goldbach conjecture.


title: Optical Spectroscopy of the environment of a ULX in NGC 7331

abstract:
  Optical photometric and spectroscopic data are presented that show an
association of an ultraluminous X-ray source in NGC 7331 with a young star
cluster of mass 1.1e5 solar masses and age 4.25 Myr. If the ULX is part of the
bright stellar cluster, then the mass of the progenitor of the compact accretor
must have been greater than about 40-50 solar masses in order to already have
evolved through the supernova stage to a compact object. The companion star is
also likely an evolved massive star. The emission line spectrum of the nebula
surrounding the cluster can be interpreted as a result of photoionization by
the cluster OB stars with an additional source of shock excitation producing
strong [SII], [OI] and NII lines. This additional source appears to be as much
as five times more powerful than the supernovae and stellar winds in the
cluster can provide. Additional mechanical energy input associated with the ULX
itself can help explain the residual shock excited line luminosities of the
emission region.


title:
Relativistic Jets and Long-Duration Gamma-ray Bursts from the Birth of
  Magnetars

abstract:
  We present time-dependent axisymmetric magnetohydrodynamic simulations of the
interaction of a relativistic magnetized wind produced by a proto-magnetar with
a surrounding stellar envelope, in the first $\sim 10$ seconds after core
collapse. We inject a super-magnetosonic wind with $\dot E = 10^{51}$ ergs
s$^{-1}$ into a cavity created by an outgoing supernova shock. A strong
toroidal magnetic field builds up in the bubble of plasma and magnetic field
that is at first inertially confined by the progenitor star. This drives a jet
out along the polar axis of the star, even though the star and the magnetar
wind are each spherically symmetric. The jet has the properties needed to
produce a long-duration gamma-ray burst (GRB). At $\sim 5$ s after core bounce,
the jet has escaped the host star and the Lorentz factor of the material in the
jet at large radii $\sim 10^{11}$ cm is similar to that in the magnetar wind
near the source. Most of the spindown power of the central magnetar escapes via
the relativistic jet. There are fluctuations in the Lorentz factor and energy
flux in the jet on $\sim 0.01-0.1$ second timescale. These may contribute to
variability in GRB emission (e.g., via internal shocks).


title: Quark Masses and Resummation in Precision QCD Theory

abstract:
  It is shown that amplitude-based, exact resummation tames the un-cancelled IR
divergences at O(alpha_s^2) in initial state radiation in QCD with massive
quarks. Implications for precision predictions for LHC physics are discussed.


title: Search for one large extra dimension with the DELPHI detector at LEP2

abstract:
  Single photons detected by the DELPHI experiment at LEP2 in the years
1997-2000 are used to investigate the existence of a single extra dimension in
a modifed ADD scenario with slightly warped large extra dimensions. The data
collected at centre-of-mass energies between 180 and 209 GeV for an integrated
luminosity of ~650 pb^-1 agree with the predictions of the Standard Model and
allow a limit to be set on graviton emission in one large extra dimension. The
limit obtained on the fundamental mass scale MD is 1.69 TeV at 95% CL, with an
expected limit of 1.71 TeV.


title:
Absolute Calibration and Characterization of the Multiband Imaging
  Photometer for Spitzer. III. An Asteroid-based Calibration of MIPS at 160
  microns

abstract:
  We describe the absolute calibration of the Multiband Imaging Photometer for
Spitzer (MIPS) 160 micron channel. After the on-orbit discovery of a near-IR
ghost image that dominates the signal for sources hotter than about 2000 K, we
adopted a strategy utilizing asteroids to transfer the absolute calibrations of
the MIPS 24 and 70 micron channels to the 160 micron channel. Near-simultaneous
observations at all three wavelengths are taken, and photometry at the two
shorter wavelengths is fit using the Standard Thermal Model. The 160 micron
flux density is predicted from those fits and compared with the observed 160
micron signal to derive the conversion from instrumental units to surface
brightness. The calibration factor we derive is 41.7 MJy/sr/MIPS160 (MIPS160
being the instrumental units). The scatter in the individual measurements of
the calibration factor, as well as an assesment of the external uncertainties
inherent in the calibration, lead us to adopt an uncertainty of 5.0
MJy/sr/MIPS160 (12%) for the absolute uncertainty on the 160 micron flux
density of a particular source as determined from a single measurement. For
sources brighter than about 2 Jy, non-linearity in the response of the 160
micron detectors produces an under-estimate of the flux density: for objects as
bright as 4 Jy, measured flux densities are likely to be ~20% too low. This
calibration has been checked against that of ISO (using ULIRGS) and IRAS (using
IRAS-derived diameters), and is consistent with those at the 5% level.


title:
Spin-glass state of vortices in YBa2Cu3Oy and La2-xSrxCuO4 below the
  metal-to-insulator crossover

abstract:
  Highly disordered magnetism confined to individual weakly interacting
vortices is detected by muon spin rotation in two different families of
high-transition-temperature superconductors, but only in samples on the
low-doping side of the low-temperature normal state metal-to-insulator
crossover (MIC). The results support an extended quantum phase transition (QPT)
theory of competing magnetic and superconducting orders that incorporates the
coupling between CuO2 planes. Contrary to what has been inferred from previous
experiments, the static magnetism that coexists with superconductivity near the
field-induced QPT is not ordered. Our findings unravel the mystery of the MIC
and establish that the normal state of high-temperature superconductors is
ubiquitously governed by a magnetic quantum critical point in the
superconducting phase.


title: A model for cyclotron resonance scattering features

abstract:
  (abbreviated version of the abstract) We study the physics of cyclotron line
formation in the high-energy spectra of accreting X-ray pulsars using Monte
Carlo methods, assuming that the line-forming region is a low-density electron
plasma in a sub-critical magnetic field. We investigate the dependence of the
shape of the fundamental line on angle, geometry, optical depth and
temperature. We also discuss variations of the line ratios for non-uniform
magnetic fields. These numerical predictions for the line profiles are linked
to results from observational data analysis using an XSPEC model based on the
Monte Carlo simulations. We apply this model to observational data from RXTE
and INTEGRAL. The predicted strong emission wings of the fundamental cyclotron
feature are not found in observational data, hinting at a bottom illuminated
slab geometry for line formation.


title: Coordinate Confusion in Conformal Cosmology

abstract:
  A straight-forward interpretation of standard
Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies is that objects move
apart due to the expansion of space, and that sufficiently distant galaxies
must be receding at velocities exceeding the speed of light. Recently, however,
it has been suggested that a simple transformation into conformal coordinates
can remove superluminal recession velocities, and hence the concept of the
expansion of space should be abandoned. This work demonstrates that such
conformal transformations do not eliminate superluminal recession velocities
for open or flat matter-only FRLW cosmologies, and all possess superluminal
expansion. Hence, the attack on the concept of the expansion of space based on
this is poorly founded. This work concludes by emphasizing that the expansion
of space is perfectly valid in the general relativistic framework, however,
asking the question of whether space really expands is a futile exercise.


title: Multiphoton antiresonance in large-spin systems

abstract:
  We study nonlinear response of a spin $S>1/2$ with easy-axis anisotropy. The
response displays sharp dips or peaks when the modulation frequency is
adiabatically swept through multiphoton resonance. The effect is a consequence
of a special symmetry of the spin dynamics in a magnetic field for the
anisotropy energy $\propto S_z^2$. The occurrence of the dips or peaks is
determined by the spin state. Their shape strongly depends on the modulation
amplitude. Higher-order anisotropy breaks the symmetry, leading to sharp steps
in the response as function of frequency. The results bear on the dynamics of
molecular magnets in a static magnetic field.


title: Supersonic flow onto a solid wedge

abstract:
  We consider the problem of 2D supersonic flow onto a solid wedge, or
equivalently in a concave corner formed by two solid walls. For mild corners,
there are two possible steady state solutions, one with a strong and one with a
weak shock emanating from the corner. The weak shock is observed in supersonic
flights. A long-standing natural conjecture is that the strong shock is
unstable in some sense.
  We resolve this issue by showing that a sharp wedge will eventually produce
weak shocks at the tip when accelerated to a supersonic speed. More precisely
we prove that for upstream state as initial data in the entire domain, the
time-dependent solution is self-similar, with a weak shock at the tip of the
wedge. We construct analytic solutions for self-similar potential flow, both
isothermal and isentropic with arbitrary $\gamma\geq 1$.
  In the process of constructing the self-similar solution, we develop a large
number of theoretical tools for these elliptic regions. These tools allow us to
establish large-data results rather than a small perturbation. We show that the
wave pattern persists as long as the weak shock is supersonic-supersonic; when
this is no longer true, numerics show a physical change of behaviour. In
addition we obtain rather detailed information about the elliptic region,
including analyticity as well as bounds for velocity components and shock
tangents.


title: Bose-Einstein condensation in an optical lattice

abstract:
  In this paper we develop an analytic expression for the critical temperature
for a gas of ideal bosons in a combined harmonic lattice potential, relevant to
current experiments using optical lattices. We give corrections to the critical
temperature arising from effective mass modifications of the low energy
spectrum, finite size effects and excited band states. We compute the critical
temperature using numerical methods and compare to our analytic result. We
study condensation in an optical lattice over a wide parameter regime and
demonstrate that the critical temperature can be increased or reduced relative
to the purely harmonic case by adjusting the harmonic trap frequency. We show
that a simple numerical procedure based on a piecewise analytic density of
states provides an accurate prediction for the critical temperature.


title: Monodromy of the p-rank strata of the moduli space of curves

abstract:
  We compute the Z/\ell and \ell-adic monodromy of every irreducible component
of the moduli space M_g^f of curves of genus and and p-rank f. In particular,
we prove that the Z/\ell-monodromy of every component of M_g^f is the
symplectic group Sp_{2g}(Z/\ell) if g>=3 and \ell is a prime distinct from p.
We give applications to the generic behavior of automorphism groups, Jacobians,
class groups, and zeta functions of curves of given genus and p-rank.


title: Strong Electron-Hole Exchange in Coherently Coupled Quantum Dots

abstract:
  We have investigated few-body states in vertically stacked quantum dots. Due
to small inter-dot tunneling rate, the coupling in our system is in a
previously unexplored regime where electron-hole exchange is the dominant spin
interaction. By tuning the gate bias, we are able to turn this coupling off and
study a complementary regime where total electron spin is a good quantum
number. The use of differential transmission allows us to obtain unambiguous
signatures of the interplay between electron and hole spin interactions. Small
tunnel coupling also enables us to demonstrate all-optical charge sensing,
where conditional exciton energy shift in one dot identifies the charging state
of the coupled partner.


title:
Carrier Multiplication in Nanocrystals via Photostimulated Generation of
  Biexcitons from Vacuum

abstract:
  We propose a novel mechanism for photogeneration of multiexcitons by single
photons (carrier multiplication) in semiconductor nanocrystals. In this
mechanism, the Coulomb interaction between two valence-band electrons involving
their transfer to the conduction band creates a virtual biexciton from vacuum
that is then converted into a real biexciton by photon absorption on an
intraband optical transition. This mechanism is inactive in bulk semiconductors
as momentum conservation suppresses intraband absorption. However, it becomes
highly efficient in zero-dimensional nanocrystals and can provide a significant
contribution to carrier multiplication in these materials.


title:
Exact Computation of Minimum Sample Size for Estimation of Binomial
  Parameters

abstract:
  It is a common contention that it is an ``impossible mission'' to exactly
determine the minimum sample size for the estimation of a binomial parameter
with prescribed margin of error and confidence level. In this paper, we
investigate such a very old but also extremely important problem and
demonstrate that the difficulty for obtaining the exact solution is not
insurmountable. Unlike the classical approximate sample size method based on
the central limit theorem, we develop a new approach for computing the minimum
sample size that does not require any approximation. Moreover, our approach
overcomes the conservatism of existing rigorous sample size methods derived
from Bernoulli's theorem or Chernoff bounds.
  Our computational machinery consists of two essential ingredients. First, we
prove that the minimum of coverage probability with respect to a binomial
parameter bounded in an interval is attained at a discrete set of finite many
values of the binomial parameter. This allows for reducing infinite many
evaluations of coverage probability to finite many evaluations. Second, a
recursive bounding technique is developed to further improve the efficiency of
computation.


title:
Orbit equivalence of topological Markov shifts and Cuntz-Krieger
  algebras

abstract:
  We will prove that one-sided topological Markov shifts $(X_A,\sigma_A)$ and
$(X_B,\sigma_B)$ for matrices $A$ and $B$ with entries in $\{0,1\}$ are
topologically orbit equivalent if and only if there exists an isomorphism
between the Cuntz-Krieger algebras ${\Cal O}_A$ and ${\Cal O}_B$ keeping their
commutative $C^*$-subalgerbas $C(X_A)$ and $C(X_B)$. It is also equivalent to
the condition that there exists a homeomorphism from $X_A$ to $X_B$
intertwining their topological full groups. We will also study structure of the
automorphisms of ${\Cal O}_A$ keeping the commutative $C^*$-algebra $C(X_A)$.


title:
Exact Computation of Minimum Sample Size for Estimating Proportion of
  Finite Population

abstract:
  In this paper, we develop an exact method for the determination of the
minimum sample size for estimating the proportion of a finite population with
prescribed margin of error and confidence level. By characterizing the behavior
of the coverage probability with respect to the proportion, we show that the
computational complexity can be significantly reduced and bounded regardless
population size.


title:
Exact Computation of Minimum Sample size for Estimation of Poisson
  Parameters

abstract:
  In this paper, we develop an approach for the exact determination of the
minimum sample size for the estimation of a Poisson parameter with prescribed
margin of error and confidence level. The exact computation is made possible by
reducing infinite many evaluations of coverage probability to finite many
evaluations. Such reduction is based on our discovery that the minimum of
coverage probability with respect to a Poisson parameter bounded in an interval
is attained at a discrete set of finite many values.


title: Cycle lengths in sparse graphs

abstract:
  Let C(G) denote the set of lengths of cycles in a graph G. In the first part
of this paper, we study the minimum possible value of |C(G)| over all graphs G
of average degree d and girth g. Erdos conjectured that |C(G)|
=\Omega(d^{\lfloor (g-1)/2\rfloor}) for all such graphs, and we prove this
conjecture. In particular, the longest cycle in a graph of average degree d and
girth g has length \Omega(d^{\lfloor (g-1)/2\rfloor}). The study of this
problem was initiated by Ore in 1967 and our result improves all previously
known lower bounds on the length of the longest cycle. Moreover, our bound
cannot be improved in general, since known constructions of d-regular Moore
Graphs of girth g have roughly that many vertices. We also show that
\Omega(d^{\lfloor (g-1)/2\rfloor}) is a lower bound for the number of odd cycle
lengths in a graph of chromatic number d and girth g. Further results are
obtained for the number of cycle lengths in H-free graphs of average degree d.
  In the second part of the paper, motivated by the conjecture of Erdos and
Gyarfas that every graph of minimum degree at least three contains a cycle of
length a power of two, we prove a general theorem which gives an upper bound on
the average degree of an n-vertex graph with no cycle of even length in a
prescribed infinite sequence of integers. For many sequences, including the
powers of two, our theorem gives the upper bound e^{O(\log^* n)} on the average
degree of graph of order n with no cycle of length in the sequence, where
\log^* n is the number of times the binary logarithm must be applied to n to
get a number which is at most


title:
A formula for a quartic integral: a survey of old proofs and some new
  ones

abstract:
  We discuss several existing proofs of the value of a quartic integral and
present a new proof that evolved from rational Landen transformations.


title: The 2-adic valuation of a sequence arising from a rational integral

abstract:
  We analyze properties of the 2-adic valuations of an integer sequence that
originates from an explicit evaluation of a quartic integral. We also give a
combinatorial interpretation of the valuations of this sequence. Connections
with the orbits arising from the Collatz (3x+1) problem are discussed.


title: Dineutron structure in $^{8}$He

abstract:
  The ground and excited states of $^{8}$He were investigated with a method of
antisymmetrized molecular dynamics(AMD). We adopted effective nuclear
interactions which systematically reproduce the binding energies of $^4$He,
$^6$He and $^8$He. The ground state of $^8$He has both the $j$-$j$ coupling
feature($p_{3/2}$ closure) and the $L$-$S$ coupling feature($^4$He$+2n+2n$)
with a slight tail of dineutron at the long distance region. The theoretical
results give an indication of the $0^+_2$ state with dineutron gas-like
structure. The dineutron structure, $^4$He+$2n$+$2n$, of this state is similar
to the $3\alpha$-cluster structure of the $^{12}$C($0^+_2$) state which has
been interpreted as an $\alpha$ condensate state. Since the $^8$He($0^+_2$)
state has a significant overlap with the dineutron condensate wave function
where two dineutrons are moving in $S$ wave around the $\alpha$ core with a
dilute density, we suggest that this theoretically predicted $0^+_2$ state is a
candidate of the dineutron condensate state.


title: The integrals in Gradshteyn and Ryzhik. Part 6: the beta function

abstract:
  We present the evaluation of definite integrals in the classical table by I.
S. Gradshteyn and I. M. Ryzhik that can be reduced to the beta function.


title: The integrals in Gradshteyn and Ryzhik. Part 7: Elementary examples

abstract:
  The classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik
contains some elementary integrals. We discuss their evaluations.


title:
The integrals in Gradshteyn and Ryzhik. Part 8: Combinations of powers,
  exponentials and logarithms

abstract:
  We present the evaluation of some definite integrals in the classical table
by I. S. Gradshteyn and I. M. Ryzhik where the integrand is a combination of
powers, exponentials and logarithms.


title:
The integrals in Gradshteyn and Ryzhik. Part9: Combinations of
  logarithms, rational and trigonometric functions

abstract:
  The classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik
contains many definite integrals where the integrand is the product of a
rational function times the logarithm of another rational function. We begin
the systematic evaluation of these integrals.


title: The bisymplectomorphism group of a bounded symmetric domain

abstract:
  An Hermitian bounded symmetric domain in a complex vector space, given in its
circled realization, is endowed with two natural symplectic forms: the flat
form and the hyperbolic form. In a similar way, the ambient vector space is
also endowed with two natural symplectic forms: the Fubini-Study form and the
flat form. It has been shown in arXiv:math.DG/0603141 that there exists a
diffeomorphism from the domain to the ambient vector space which puts in
correspondence the above pair of forms. This phenomenon is called symplectic
duality for Hermitian non compact symmetric spaces.
  In this article, we first give a different and simpler proof of this fact.
Then, in order to measure the non uniqueness of this symplectic duality map, we
determine the group of bisymplectomorphisms of a bounded symmetric domain, that
is, the group of diffeomorphisms which preserve simultaneously the hyperbolic
and the flat symplectic form. This group is the direct product of the compact
Lie group of linear automorphisms with an infinite-dimensional Abelian group.
This result appears as a kind of Schwarz lemma.


title: On complexity of special maximum matchings constructing

abstract:
  For bipartite graphs the NP-completeness is proved for the problem of
existence of maximum matching which removal leads to a graph with given
lower(upper)bound for the cardinality of its maximum matching.


title: Influence of oxygen vacancy on the electronic structure of HfO$_2$ film

abstract:
  We investigated the unoccupied part of the electronic structure of the
oxygen-deficient hafnium oxide (HfO$_{\sim1.8}$) using soft x-ray absorption
spectroscopy at O $K$ and Hf $N_3$ edges. Band-tail states beneath the
unoccupied Hf 5$d$ band are observed in the O $K$-edge spectra; combined with
ultraviolet photoemission spectrum, this indicates the non-negligible
occupation of Hf 5$d$ state. However, Hf $N_3$-edge magnetic circular dichroism
spectrum reveals the absence of a long-range ferromagnetic spin order in the
oxide. Thus the small amount of $d$ electron gained by the vacancy formation
does not show inter-site correlation, contrary to a recent report [M.
Venkatesan {\it et al.}, Nature {\bf 430}, 630 (2004)].


title:
Entropy of the Schwarzschild black hole to all orders in the Planck
  length

abstract:
  Considering corrections to all orders in the Planck length on the quantum
state density from a generalized uncertainty principle (GUP), we calculate the
statistical entropy of the scalar field on the background of the Schwarzschild
black hole without any cutoff. We obtain the entropy of the massive scalar
field proportional to the horizon area.


title: Age Problem in the Holographic Dark Energy Model

abstract:
  In this note, we test the original holographic dark energy model with some
old high redshift objects. The main idea is very simple: the universe cannot be
younger than its constituents. We find that the original holographic dark
energy model can be ruled out, unless a lower Hubble constant is taken.


title: Gagliardo-Nirenberg inequalities on manifolds

abstract:
  We prove Gagliardo-Nirenberg inequalities on some classes of manifolds, Lie
groups and graphs.


title:
Nonequilibrium Work distributions for a trapped Brownian particle in a
  time dependent magnetic field

abstract:
  We study the dynamics of a trapped, charged Brownian particle in presence of
a time dependent magnetic field. We calculate work distributions for different
time dependent protocols. In our problem thermodynamic work is related to
variation of vector potential with time as opposed to the earlier studies where
the work is related to time variation of the potentials which depends only on
the coordinates of the particle. Using Jarzynski identity and Crook's equality
we show that the free energy of the particle is independent of the magnetic
field, thus complementing the Bohr-van Leeuwen theorem. We also show that our
system exhibits a parametric resonance in certain parameter space.


title: Unparticle Physics and Supersymmetry Phenomenology

abstract:
  We show a natural form of the interaction between unparticle and
supersymmetry. Using the couplings of unparticle to supersymmetry presented, as
examples, we calculate the differential decay rates for the processes ${\it
{\tilde f}}\to {\it f}+{\cal U}_{3/2}$, ${\it {\tilde \chi}}^0\to{\it
\gamma}+{\cal U}_{3/2}$, ${\it {\tilde \chi}}^\pm\to W^\pm+{\cal U}_{3/2}$ and
${\it {\tilde \chi}}^0\to Z^0+{\cal U}_{3/2}$. Finally, we discuss the
phenomenological implication of our results and give some comments.


title:
Martensitic transition, ferrimagnetism and Fermi surface nesting in
  Mn_2NiGa

abstract:
  The electronic structure of Mn_2NiGa has been studied using density
functional theory and photoemission spectroscopy. The lower temperature
tetragonal martensitic phase with c/a= 1.25 is more stable compared to the
higher temperature austenitic phase. Mn_2NiGa is ferrimagnetic in both phases.
The calculated valence band spectrum, the optimized lattice constants and the
magnetic moments are in good agreement with experiment. The majority-spin Fermi
surface (FS) expands in the martensitic phase, while the minority-spin FS
shrinks. FS nesting indicates occurrence of phonon softening and modulation in
the martensitic phase.


title: Semigroups on Frechet spaces and equations with infinite delays

abstract:
  In this paper, we show existence and uniqueness of a solution to a functional
differential equation with infinite delay. We choose an appropriate Frechet
space so as to cover a large class of functions to be used as initial functions
to obtain existence and uniqueness of solutions.


title: Nonconforming h-p spectral element methods for elliptic problems

abstract:
  In this paper we show that we can use a modified version of the h-p spectral
element method proposed in \cite{duttora1,duttom,duttora2,tomarth} to solve
elliptic problems with general boundary conditions to exponential accuracy on
polygonal domains using nonconforming spectral element functions. A geometrical
mesh is used in a neighbourhood of the corners. With this mesh we seek a
solution which minimizes the sum of a weighted squared norm of the residuals in
the partial differential equation and the squared norm of the residuals in the
boundary conditions in fractional Sobolev spaces and enforce continuity by
adding a term which measures the jump in the function and its derivatives at
inter-element boundaries, in fractional Sobolev norms, to the functional being
minimized. In the neighbourhood of the corners, modified polar coordinates are
used and a global coordinate system elsewhere. A stability estimate is derived
for the functional which is minimized based on the regularity estimate in
\cite{babguo1}. We examine how to parallelize the method and show that the set
of common boundary values consists of the values of the function at the corners
of the polygonal domain. The method is faster than that proposed in
\cite{duttora1,duttom,tomarth} and the h-p finite element method and stronger
error estimates are obtained.


title: Reducing system of parameters and the Cohen--Macaulay property

abstract:
  Let $R$ be a local ring and let ($x_1\biss x_r$) be part of a system of
parameters of a finitely generated $R$-module $M,$ where $r < \dim_R M$. We
will show that if ($y_1\biss y_r$) is part of a reducing system of parameters
of $M$ with $(y_1\biss y_r)M=(x_1\biss x_r)M$ then $(x_1\biss x_r)$ is already
reducing. Moreover, there is such a part of a reducing system of parameters of
$M$ iff for all primes $P\in \supp M \cap V_R(x_1\biss x_r)$ with $\dim_R R/P =
\dim_R M -r$ the localization $M_P$ of $M$ at $P$ is an $r$-dimensional \cm\
module over $R_P$. Furthermore, we will show that $M$ is a \cm module iff $y_d$
is a non zero divisor on $M/(y_1\biss y_{d-1})M$, where $(y_1\biss y_d)$ is a
reducing system of parameters of $M$ ($d := \dim_R M$).


title:
A classical model for a photodetector in the presence of electromagnetic
  vacuum fluctuations

abstract:
  The main argument against the reality of the electromagnetic vacuum
fluctuations is that they do not activate photon detectors. In order to meet
this objection we propose a classical model of a photodetector which, in the
simple case of a light signal with constant intensity, gives a counting rate
which is a non-linear function of the intensity. For sufficiently large signal
intensity, the counting rate is proportional to the intensity, in agreement
with the standard quantum results, but there is a dark rate when the signal
intensity is low.


title: Corners of normal matrices

abstract:
  We study various conditions on matrices $B$ and $C$ under which they can be
the off-diagonal blocks of a partitioned normal matrix.


title: On a Result of Hardy and Ramanujan

abstract:
  In this paper, we introduce some explicit approximations for the summation
$\sum_{k\leq n}\Omega(k)$, where $\Omega(k)$ is the total number of prime
factors of $k$.


title: Nice surjections on spaces of operators

abstract:
  A bounded linear operator is said to be nice if its adjoint preserves extreme
points of the dual unit ball. Motivated by a description due to Labuschagne and
Mascioni \cite{LM} of such maps for the space of compact operators on a Hilbert
space, in this article we consider a description of nice surjections on
${\mathcal K}(X,Y)$ for Banach spaces $X,Y$. We give necessary and sufficient
conditions when nice surjections are given by composition operators. Our
results imply automatic continuity of these maps with respect to other
topologies on spaces of operators. We also formulate the corresponding result
for ${\mathcal L}(X,Y)$ thereby proving an analogue of the result from
\cite{LM} for $L^p$ ($1 <p \neq 2 <\infty$) spaces. We also formulate results
when nice operators are not of the canonical form, extending and correcting the
results from \cite{KS}.


title: Gromov--Witten invariants and quantum cohomology

abstract:
  This article is an elaboration of a talk given at an international conference
on Operator Theory, Quantum Probability, and Noncommutative Geometry held
during December~20--23, 2004, at the Indian Statistical Institute, Kolkata. The
lecture was meant for a general audience, and also prospective research
students, the idea of the quantum cohomology based on the Gromov--Witten
invariants. Of course there are many important aspects that are not discussed
here.


title: Representations of homogeneous quantum L\'evy fields

abstract:
  We study homogeneous quantum L\'{e}vy processes and fields with independent
additive increments over a noncommutative *-monoid. These are described by
infinitely divisible generating state functionals, invariant with respect to an
endomorphic injective action of a symmetry semigroup. A strongly covariant GNS
representation for the conditionally positive logarithmic functionals of these
states is constructed in the complex Minkowski space in terms of canonical
quadruples and isometric representations on the underlying pre-Hilbert field
space. This is of much use in constructing quantum stochastic representations
of homogeneous quantum L\'{e}vy fields on It\^{o} monoids, which is a natural
algebraic way of defining dimension free, covariant quantum stochastic
integration over a space-time indexing set.


title: Malliavin calculus of Bismut type without probability

abstract: We translate in semigroup theory Bismut's way of the Malliavin calculus.


title:
Stochastic integral representations of quantum martingales on multiple
  Fock space

abstract:
  In this paper a quantum stochastic integral representation theorem is
obtained for unbounded regular martingales with respect to multidimensional
quantum noise. This simultaneously extends results of Parthasarathy and Sinha
to unbounded martingales and those of the author to multidimensions.


title: On equivariant Dirac operators for $SU_q(2)$

abstract:
  We explain the notion of minimality for an equivariant spectral triple and
show that the triple for the quantum SU(2) group constructed by Chakraborty and
Pal in \cite{c-p1} is minimal. We also give a decomposition of the spectral
triple constructed by Dabrowski {\it et al} \cite{dlssv} in terms of the
minimal triple constructed in \cite{c-p1}.


title:
Schr\"odinger operators on the half line: Resolvent expansions and the
  Fermi golden rule at thresholds

abstract:
  We consider Schr\"odinger operators $H=- \d^2/\d r^2+V$ on $L^2([0,\infty))$
with the Dirichlet boundary condition. The potential $V$ may be local or
non-local, with polynomial decay at infinity. The point zero in the spectrum of
$H$ is classified, and asymptotic expansions of the resolvent around zero are
obtained, with explicit expressions for the leading coefficients. These results
are applied to the perturbation of an eigenvalue embedded at zero, and the
corresponding modified form of the Fermi golden rule.


title: Generators of Detailed Balance Quantum Markov Semigroups

abstract:
  For a quantum Markov semigroup $\T$ on the algebra $\B$ with a faithful
invariant state $\rho$, we can define an adjoint $\widetilde{\T}$ with respect
to the scalar product determined by $\rho$. In this paper, we solve the open
problems of characterising adjoints $\widetilde{\T}$ that are also a quantum
Markov semigroup and satisfy the detailed balance condition in terms of the
operators $H,L_k$ in the Gorini Kossakowski Sudarshan Lindblad representation
$\Ll(x)=i[H,x] - {1/2}\sum_k(L^*_kL_k x-2L^*_kxL_k + xL^*_kL_k)$ of the
generator of $\T$. We study the adjoint semigroup with respect to both scalar
products $<a,b> = \tr(\rho a^* b)$ and $<a,b> = \tr(\rho^{1/2} a^*
\rho^{1/2}b)$.


title: Reducible family of height three level algebras

abstract:
  Let $R=k[x_1,..., x_r]$ be the polynomial ring in $r$ variables over an
infinite field $k$, and let $M$ be the maximal ideal of $R$. Here a \emph{level
algebra} will be a graded Artinian quotient $A$ of $R$ having socle
$Soc(A)=0:M$ in a single degree $j$. The Hilbert function $H(A)=(h_0,h_1,...
,h_j)$ gives the dimension $h_i=\dim_k A_i$ of each degree-$i$ graded piece of
$A$ for $0\le i\le j$. The embedding dimension of $A$ is $h_1$, and the
\emph{type} of $A$ is $\dim_k \Soc (A)$, here $h_j$. The family $\Levalg (H)$
of level algebra quotients of $R$ having Hilbert function $H$ forms an open
subscheme of the family of graded algebras or, via Macaulay duality, of a
Grassmannian.
  We show that for each of the Hilbert functions $H=H_1=(1,3,4,4)$ and
$H=H_2=(1,3,6,8,9,3)$ the family $LevAlg (H)$ parametrizing level Artinian
algebras of Hilbert function $H$ has several irreducible components. We show
also that these examples each lift to points. However, in the first example, an
irreducible Betti stratum for Artinian algebras becomes reducible when lifted
to points. These were the first examples we obtained of multiple components for
$\Levalg(H)$ in embedding dimension three.
  We also show that the second example is the first in an infinite sequence of
examples of type three Hilbert functions $H(c)$ in which also the number of
components of LevAlg(H) gets arbitrarily large.
  The first case where the phenomenon of multiple components can occur (i.e.
the lowest embedding dimension and then the lowest type) is that of dimension
three and type two. Examples of this first case have been obtained by the
authors and also by J.-O. Kleppe.


title:
Dispersion relations in quantum electrodynamics on the noncommutative
  Minkowski space

abstract:
  We study field theories on the noncommutative Minkowski space with
noncommuting time. The focus lies on dispersion relations in quantized
interacting models in the Yang-Feldman formalism. In particular, we compute the
two-point correlation function of the field strength in noncommutative quantum
electrodynamics to second order. At this, we take into account the covariant
coordinates that allow the construction of local gauge invariant quantities
(observables). It turns out that this does not remove the well-known severe
infrared problem, as one might have hoped. Instead, things become worse, since
nonlocal divergences appear. We also show that these cancel in a supersymmetric
version of the theory if the covariant coordinates are adjusted accordingly.
  Furthermore, we study the phi^3 and the Wess-Zumino model and show that the
distortion of the dispersion relations is moderate for parameters typical for
the Higgs field. We also disuss the formulation of gauge theories on
noncommutative spaces and study classical electrodynamics on the noncommutative
Minkowski space using covariant coordinates. In particular, we compute the
change of the speed of light due to nonlinear effects in the presence of a
background field. Finally, we examine the so-called twist approach to quantum
field theory on the noncommutative Minkowski space and point out some
conceptual problems of this approach.


title: On the Symmetric Space Sigma-Model Kinematics

abstract:
  The solvable Lie algebra parametrization of the symmetric spaces is
discussed. Based on the solvable Lie algebra gauge two equivalent formulations
of the symmetric space sigma model are studied. Their correspondence is
established by inspecting the normalization conditions and deriving the field
transformation laws.


title: Local representations of the quantum Teichmuller space

abstract:
  We introduce a certain type of representations for the quantum Teichmuller
space of a punctured surface, which we call local representations. We show
that, up to finitely many choices, these purely algebraic representations are
classified by classical geometric data. We also investigate the family of
intertwining operators associated to such a representations. In particular, we
use these intertwiners to construct a natural fiber bundle over the Teichmuller
space and its quotient under the action of the mapping class group. This
construction also offers a convenient framework to exhibit invariants of
surface diffeomorphisms.


title: Weiss oscillations in the electronic structure of modulated graphene

abstract:
  We present a theoretical study of the electronic structure of modulated
graphene in the presence of a perpendicular magnetic field. The density of
states and the bandwidth for the Dirac electrons in this system are determined.
The appearance of unusual Weiss oscillations in the bandwidth and density of
states is the main focus of this work.