title: Culminating paths

abstract:
  Let a and b be two positive integers. A culminating path is a path of Z^2
that starts from (0,0), consists of steps (1,a) and (1,-b), stays above the
x-axis and ends at the highest ordinate it ever reaches. These paths were first
encountered in bioinformatics, in the analysis of similarity search algorithms.
They are also related to certain models of Lorentzian gravity in theoretical
physics. We first show that the language on a two letter alphabet that
naturally encodes culminating paths is not context-free. Then, we focus on the
enumeration of culminating paths. A step by step approach, combined with the
kernel method, provides a closed form expression for the generating fucntion of
culminating paths ending at a (generic) height k. In the case a=b, we derive
from this expression the asymptotic behaviour of the number of culminating
paths of length n. When a>b, we obtain the asymptotic behaviour by a simpler
argument. When a<b, we only determine the exponential growth of the number of
culminating paths. Finally, we study the uniform random generation of
culminating paths via various methods. The rejection approach, coupled with a
symmetry argument, gives an algorithm that is linear when a>= b, with no
precomputation stage nor non-linear storage required. The choice of the best
algorithm is not as clear when a<b. An elementary recursive approach yields a
linear algorithm after a precomputation stage involving O(n^3) arithmetic
operations, but we also present some alternatives that may be more efficient in
practise.


title:
Finite temperature phase transition of a single scalar field on a fuzzy
  sphere

abstract:
  We study finite temperature phase transition of neutral scalar field on a
fuzzy sphere using Monte Carlo simulations. We work with the zero mode in the
temporal directions, while the effects of the higher modes are taken care by
the temperature dependence of r. In the numerical calculations we use
"pseudo-heatbath" method which reduces the auto-correlation considerably. Our
results agree with the conventional calculations. We report some new results
which show the presence of meta-stable states and also suggest that for
suitable choice of parameters the symmetry breaking transition is of first
order.


title: Probing the dynamical state of galaxy clusters

abstract:
  We show how hydrostatic equilibrium in galaxy clusters can be quantitatively
probed combining X-ray, SZ, and gravitational-lensing data. Our previously
published method for recovering three-dimensional cluster gas distributions
avoids the assumption of hydrostatic equilibrium. Independent reconstructions
of cumulative total-mass profiles can then be obtained from the gas
distribution, assuming hydrostatic equilibrium, and from gravitational lensing,
neglecting it. Hydrostatic equilibrium can then be quantified comparing the
two. We describe this procedure in detail and show that it performs well on
progressively realistic synthetic data. An application to a cluster merger
demonstrates how hydrostatic equilibrium is violated and restored as the merger
proceeds.


title: Higher order antibunching in intermediate states

abstract:
  Since the introduction of binomial state as an intermediate state, different
intermediate states have been proposed. Different nonclassical effects have
also been reported in these intermediate states. But till now higher order
antibunching or higher order subpoissonian photon statistics is predicted only
in one type of intermediate state, namely shadowed negative binomial state.
Recently we have shown the existence of higher order antibunching in some
simple nonlinear optical processes to establish that higher order antibunching
is not a rare phenomenon (J. Phys. B 39 (2006) 1137). To establish our earlier
claim further, here we have shown that the higher order antibunching can be
seen in different intermediate states, such as binomial state, reciprocal
binomial state, hypergeometric state, generalized binomial state, negative
binomial state and photon added coherent state. We have studied the possibility
of observing the higher order subpoissonian photon statistics in different
limits of intermediate states. The effect of different control parameters have
also been studied in this connection and it has been shown that the depth of
nonclassicality can be tuned by controlling various physical parameters.


title:
Thermal effects on nuclear symmetry energy with a momentum-dependent
  effective interaction

abstract:
  The knowledge of the nuclear symmetry energy of hot neutron-rich matter is
important for understanding the dynamical evolution of massive stars and the
supernova explosion mechanisms. In particular, the electron capture rate on
nuclei and/or free protons in presupernova explosions is especially sensitive
to the symmetry energy at finite temperature. In view of the above, in the
present work we calculate the symmetry energy as a function of the temperature
for various values of the baryon density, by applying a momentum-dependent
effective interaction. In addition to a previous work, the thermal effects are
studied separately both in the kinetic part and the interaction part of the
symmetry energy. We focus also on the calculations of the mean field potential,
employed extensively in heavy ion reaction research, both for nuclear and pure
neutron matter. The proton fraction and the electron chemical potential, which
are crucial quantities for representing the thermal evolution of supernova and
neutron stars, are calculated for various values of the temperature. Finally,
we construct a temperature dependent equation of state of $\beta$-stable
nuclear matter, the basic ingredient for the evaluation of the neutron star
properties.


title:
A Liouville type theorem for special Lagrangian Equations with
  constraints

abstract:
  We derive a Liouville type result for special Lagrangian equations with
certain "convexity" and restricted linear growth assumptions on the solutions.


title: Planar Josephson Tunnel Junctions in a Transverse Magnetic Field

abstract:
  Traditionally, since the discovery of the Josephson effect in 1962, the
magnetic diffraction pattern of planar Josephson tunnel junctions has been
recorded with the field applied in the plane of the junction. Here we discuss
the static junction properties in a transverse magnetic field where
demagnetization effects imposed by the junction geometry and configuration of
the electrodes are important. Measurements of the critical current versus
magnetic field in planar Nb-based high-quality junctions with different
geometry, size and critical current density show that it is advantageous to use
a transverse magnetic field rather than an in-plane field to suppress the
Josephson tunnel current and Fiske resonances in practical applications.


title: Top Pair Production cross-section at the Tevatron

abstract:
  An overview of latest top quark pair production cross-sections measured at
the Tevatron is given. These measurements have been carried out in the
dilepton, lepton+jets and all-jets channels with an integrated luminosity of
about 1fb-1. The measurements are consistent with NNLO calculations.


title: The sum-product estimate for large subsets of prime fields

abstract:
  Let $\mathbb{F}_p$ be the field of a prime order $p.$ It is known that for
any integer $N\in [1,p]$ one can construct a subset $A\subset\mathbb{F}_p$ with
$|A|= N$ such that $$ \max\{|A+A|, |AA|\}\ll p^{1/2}|A|^{1/2}. $$ In the
present paper we prove that if $A\subset \mathbb{F}_p$ with $|A|>p^{2/3},$ then
$$ \max\{|A+A|, |AA|\}\gg p^{1/2}|A|^{1/2}. $$


title: Some naturally ocurring examples of A-infinity bialgebras

abstract:
  Let p be an odd prime. When n>2, we show that each tensor factor of form E
\otimes \Gamma in H(Z,n;Z_p) is an A-infinity bialgebra with non-trivial
structure. We give explicit formulas for the structure maps and the quadratic
relations among them. Thus E \otimes \Gamma is a naturally occurring example of
an A-infinity bialgebra whose internal structure is well-understood.


title: Strong field effects on binary systems in Einstein-aether theory

abstract:
  "Einstein-aether" theory is a generally covariant theory of gravity
containing a dynamical preferred frame. This article continues an examination
of effects on the motion of binary pulsar systems in this theory, by
incorporating effects due to strong fields in the vicinity of neutron star
pulsars. These effects are included through an effective approach, by treating
the compact bodies as point particles with nonstandard, velocity dependent
interactions parametrized by dimensionless "sensitivities". Effective
post-Newtonian equations of motion for the bodies and the radiation damping
rate are determined. More work is needed to calculate values of the
sensitivities for a given fluid source, so precise constraints on the theory's
coupling constants cannot yet be stated. It is shown, however, that strong
field effects will be negligible given current observational uncertainties if
the dimensionless couplings are less than roughly 0.01 and two conditions that
match the PPN parameters to those of pure general relativity are imposed. In
this case, weak field results suffice and imply one further condition on the
couplings. Thus, there exists a one-parameter family of Einstein-aether
theories with "small-enough" couplings that passes all current observational
tests. No conclusion can yet be reached for large couplings.


title: On the dimension of subspaces with bounded Schmidt rank

abstract:
  We consider the question of how large a subspace of a given bipartite quantum
system can be when the subspace contains only highly entangled states. This is
motivated in part by results of Hayden et al., which show that in large d x
d--dimensional systems there exist random subspaces of dimension almost d^2,
all of whose states have entropy of entanglement at least log d - O(1). It is
also related to results due to Parthasarathy on the dimension of completely
entangled subspaces, which have connections with the construction of
unextendible product bases. Here we take as entanglement measure the Schmidt
rank, and determine, for every pair of local dimensions dA and dB, and every r,
the largest dimension of a subspace consisting only of entangled states of
Schmidt rank r or larger. This exact answer is a significant improvement on the
best bounds that can be obtained using random subspace techniques. We also
determine the converse: the largest dimension of a subspace with an upper bound
on the Schmidt rank. Finally, we discuss the question of subspaces containing
only states with Schmidt equal to r.


title:
The Common Origin of Linear and Nonlinear Chiral Multiplets in N=4
  Mechanics

abstract:
  Elaborating on previous work (hep-th/0605211, hep-th/0611247), we show how
the linear and nonlinear chiral multiplets of N=4 supersymmetric mechanics with
the off-shell content (2,4,2) can be obtained by gauging three distinct
two-parameter isometries of the ``root'' (4,4,0) multiplet actions. In
particular, two different gauge groups, one abelian and one non-abelian, lead,
albeit in a disguised form in the second case, to the same (unique) nonlinear
chiral multiplet. This provides an evidence that no other nonlinear chiral N=4
multiplets exist. General sigma model type actions are discussed, together with
the restricted potential terms coming from the Fayet-Iliopoulos terms
associated with abelian gauge superfields. As in our previous work, we use the
manifestly supersymmetric language of N=4, d=1 harmonic superspace. A novel
point is the necessity to use in parallel the \lambda and \tau gauge frames,
with the ``bridges'' between these two frames playing a crucial role. It is the
N=4 harmonic analyticity which, though being non-manifest in the \tau frame,
gives rise to both linear and nonlinear chirality constraints.


title: Contact metric $(\kappa,\mu)$-spaces as bi-Legendrian manifolds

abstract:
  We regard a contact metric manifold whose Reeb vector field belongs to the
$(\kappa,\mu)$-nullity distribution as a bi-Legendrian manifold and we study
its canonical bi-Legendrian structure. Then we characterize contact metric
$(\kappa,\mu)$-spaces in terms of a canonical connection which can be naturally
defined on them.


title: The topology of the spectrum for Gelfand pairs on Lie groups

abstract:
  Given a Gelfand pair of Lie groups, we identify the spectrum with a suitable
subset of C^n and we prove the equivalence between Gelfand topology and
euclidean topology.


title: Spin-charge separation in two-component Bose-gases

abstract:
  We show that one of the key characteristics of interacting one-dimensional
electronic quantum systems, the separation of spin and charge, can be observed
in a two-component system of bosonic ultracold atoms even close to a competing
phase separation regime. To this purpose we determine the real-time evolution
of a single particle excitation and the single-particle spectral function using
density-matrix renormalization group techniques. Due to efficient bosonic
cooling and good tunability this setup exhibits very good conditions for
observing this strong correlation effect. In anticipation of experimental
realizations we calculate the velocities for spin and charge perturbations for
a wide range of parameters.


title: Ultrarelativistic N-boson systems

abstract:
  General analytic energy bounds are derived for N-boson systems governed by
ultrarelativistic Hamiltonians of the form
  H = sum_{i=1}^N||p_i|| + sum_{1=i<j}^N V(r_{ij}), where V(r) is a static
attractive pair potential. It is proved that a translation-invariant model
Hamiltonian H_c provides a lower bound to H for all N \ge 2. This result was
conjectured in an earlier paper but proved only for N = 2,3,4. As an example,
the energy in the case of the linear potential V(r) = r is determined with
error less than 0.55% for all N \ge 2.


title: A categorical framework for the quantum harmonic oscillator

abstract:
  This paper describes how the structure of the state space of the quantum
harmonic oscillator can be described by an adjunction of categories, that
encodes the raising and lowering operators into a commutative comonoid. The
formulation is an entirely general one in which Hilbert spaces play no special
role. Generalised coherent states arise through the hom-set isomorphisms
defining the adjunction, and we prove that they are eigenstates of the lowering
operators. Surprisingly, generalised exponentials also emerge naturally in this
setting, and we demonstrate that coherent states are produced by the
exponential of a raising morphism acting on the zero-particle state. Finally,
we examine all of these constructions in a suitable category of Hilbert spaces,
and find that they reproduce the conventional mathematical structures.


title: First Order Description of Black Holes in Moduli Space

abstract:
  We show that the second order field equations characterizing extremal
solutions for spherically symmetric, stationary black holes are in fact implied
by a system of first order equations given in terms of a prepotential W. This
confirms and generalizes the results in [14]. Moreover we prove that the
squared prepotential function shares the same properties of a c-function and
that it interpolates between M^2_{ADM} and M^2_{BR}, the parameter of the
near-horizon Bertotti-Robinson geometry. When the black holes are solutions of
extended supergravities we are able to find an explicit expression for the
prepotentials, valid at any radial distance from the horizon, which reproduces
all the attractors of the four dimensional N>2 theories. Far from the horizon,
however, for N-even our ansatz poses a constraint on one of the U-duality
invariants for the non-BPS solutions with Z \neq 0. We discuss a possible
extension of our considerations to the non extremal case.


title: On the robustness of H-deficient post-AGB tracks

abstract:
  We analyze the robustness of H--deficient post--AGB tracks regarding previous
evolution of their progenitor stars and the constitutive physics of the
remnants. Our motivation is a recent suggestion of Werner & Herwig (2006) that
previous evolution should be important in shaping the final post--AGB track and
the persisting discrepancy between asteroseismological and spectroscopical mass
determinations. This work is thus complementary to our previous work (Miller
Bertolami & Althaus 2006) and intends to shed some light on the uncertainty
behind the evolutionary tracks presented there. We compute full evolutionary
models for PG1159 stars taking into account different extramixing
(overshooting) efficiencies and lifetimes on the TP-AGB during the progenitor
evolution. We also assess the effect of possible differences in the opacities
and equation of state by artificially changing them before the PG1159 stage.
Also comparisons are made with the few H-deficient post--AGB tracks available
in the literature. Contrary to our expectations, we found that previous
evolution is not a main factor in shaping H--deficient post--AGB tracks.
Interestingly enough, we find that only an increase of $\sim50%$ in the
intershell opacities at high effective temperatures may affect the tracks as to
reconcile spectroscopic and asteroseismologic mass determinations. This forces
us to conclude that our previous tracks (Miller Bertolami & Althaus 2006) are
robust enough as to be used for spectroscopic mass determinations, unless
opacities in the intershell region are substantially different. Our results,
then, call for an analysis of possible systematics in the usually adopted
asteroseismological mass determination methods.


title:
The born again (VLTP) scenario revisited: The mass of the remnants and
  implications for V4334 Sgr

abstract:
  We present 1-D numerical simulations of the very late thermal pulse
  (VLTP) scenario for a wide range of remnant masses. We show that by taking
into account the different possible remnant masses, the observed evolution of
V4334 Sgr (a.k.a. Sakurai's Object) can be reproduced within the standard
1D-MLT stellar evolutionary models without the inclusion of any $ad-hoc$
reduced mixing efficiency. Our simulations hint at a consistent picture with
present observations of V4334 Sgr. From energetics, and within the standard MLT
approach, we show that low mass remnants \hbox{($M\lesssim0.6$\msun)} are
expected to behave markedly different than higher mass remnants
\hbox{($M\gtrsim0.6$\msun)} in the sense that the latter are not expected to
expand significantly as a result of the violent H-burning that takes place
during the VLTP. We also assess the discrepancy in the born again times
obtained by different authors by comparing the energy that can be liberated by
H-burning during the VLTP event.


title: Standard vs. Reduced Genus-One Gromov-Witten Invariants

abstract:
  We give an explicit formula for the difference between the standard and
reduced genus-one Gromov-Witten invariants. Combined with previous work on
geometric properties of the latter, this paper makes it possible to compute the
standard genus-one GW-invariants of complete intersections. In particular, we
obtain a closed formula for the genus-one GW-invariants of a Calabi-Yau
projective hypersurface and verify a recent mirror symmetry prediction for a
sextic fourfold as a special case.


title: Partition theory: A very simple illustration

abstract:
  We illustrate the main features of a recently proposed method based on
ensemble density functional theory to divide rigorously a complex molecular
system into its parts [M.H. Cohen and A. Wasserman, J. Phys. Chem. A 111, 2229
(2007)]. The illustrative system is an analog of the hydrogen molecule for
which analytic expressions for the densities of the parts (hydrogen "atoms")
are found along with the "reactivity potential" that enters the theory. While
previous formulations of Chemical Reactivity Theory lead to zero, or undefined,
values for the chemical hardness of the isolated parts, we demonstrate they can
acquire a finite and positive hardness within the present formulation.


title: Marginal deformation for the photon in superstring field theory

abstract:
  We find solutions of supersymmetric string field theory that correspond to
the photon marginal deformation in the boundary conformal field theory. We
revisit the bosonic string marginal deformation and generate a real solution
for it. We find a map between the solutions of bosonic and supersymmetric
string field theories and suggest a universal solution to superstring field
theory.


title: Recent charm results from CLEO-c

abstract:
  The CLEO-c experiment has been collecting data at the charm-threshold region.
A selection of recent results on charmed meson and charmonia decays are
presented.


title:
Self-Phasematched Nonlinear Optics in Integrated Semiconductor
  Microcavities

abstract:
  A novel concept of self-phasematched optical frequency conversion in
dispersive dielectric microcavities is studied theoretically and
experimentally. We develop a time-dependent model, incorporating the dispersion
into the structure of the spatial cavity modes and translating the
phasematching requirement into the optimization of a nonlinear cavity mode
overlap. We design and fabricate integrated double-resonance semiconductor
microcavities for self-phasematched second harmonic generation. The measured
efficiency exhibits a significant maximum near the cavity resonance due to the
intra-cavity enhancement of the input power and the dispersion-induced
wavelength detuning effect on the mode overlap, in good agreement with our
theoretical predictions.


title:
Universal Quantile Estimation with Feedback in the
  Communication-Constrained Setting

abstract:
  We consider the following problem of decentralized statistical inference:
given i.i.d. samples from an unknown distribution, estimate an arbitrary
quantile subject to limits on the number of bits exchanged. We analyze a
standard fusion-based architecture, in which each of $m$ sensors transmits a
single bit to the fusion center, which in turn is permitted to send some number
$k$ bits of feedback. Supposing that each of $\nodenum$ sensors receives $n$
observations, the optimal centralized protocol yields mean-squared error
decaying as $\order(1/[n m])$. We develop and analyze the performance of
various decentralized protocols in comparison to this centralized
gold-standard. First, we describe a decentralized protocol based on $k =
\log(\nodenum)$ bits of feedback that is strongly consistent, and achieves the
same asymptotic MSE as the centralized optimum. Second, we describe and analyze
a decentralized protocol based on only a single bit ($k=1$) of feedback. For
step sizes independent of $m$, it achieves an asymptotic MSE of order
$\order[1/(n \sqrt{m})]$, whereas for step sizes decaying as $1/\sqrt{m}$, it
achieves the same $\order(1/[n m])$ decay in MSE as the centralized optimum.
Our theoretical results are complemented by simulations, illustrating the
tradeoffs between these different protocols.


title: The Jacobian algebras

abstract:
  The Jacobian algebras are introduced and their various properties are
studied.


title: An ansatz for the asymptotics of hypergeometric multisums

abstract:
  Sequences that are defined by multisums of hypergeometric terms with compact
support occur frequently in enumeration problems of combinatorics, algebraic
geometry and perturbative quantum field theory. The standard recipe to study
the asymptotic expansion of such sequences is to find a recurrence satisfied by
them, convert it into a differential equation satisfied by their generating
series, and analyze the singulatiries in the complex plane. We propose a
shortcut by constructing directly from the structure of the hypergeometric term
a finite set, for which we conjecture (and in some cases prove) that it
contains all the singularities of the generating series. Our construction of
this finite set is given by the solution set of a balanced system of polynomial
equations of a rather special form, reminiscent of the Bethe ansatz. The finite
set can also be identified with the set of critical values of a potential
function, as well as with the evaluation of elements of an additive $K$-theory
group by a regulator function. We give a proof of our conjecture in some
special cases, and we illustrate our results with numerous examples.


title:
On simple arrangements of lines and pseudo-lines in P^2 and R^2 with the
  maximum number of triangles

abstract:
  We give some new advances in the research of the maximum number of triangles
that we may obtain in a simple arrangements of n lines or pseudo-lines.


title: Resonance Production in Jet

abstract:
  Hadronic resonances with short life times and strong coupling to the dense
medium may exhibit mass shifts and width broadening as signatures of chiral
symmetry restoration at the phase transition between hadronic and partonic
matter. Resonances with different lifetimes are also used to extract
information about the time evolution and temperature of the expanding hadronic
medium. In order to collect information about the early stage (at the phase
transition) of a heavy-ion collision, resonances and decay particles which are
unaffected by the hadronic medium have to be used. We explore a possible new
technique to extract signals from the early stage through the selection of
resonances from jets. A first attempt of this analysis, using the reconstructed
$\phi$(1020) from 200 GeV Au+Au collisions in STAR, is presented.


title:
Factorization of quadratic polynomials in the ring of formal power
  series over $\Z$

abstract:
  We establish necessary and sufficient conditions for a quadratic polynomial
to be irreducible in the ring $Z[[x]]$ of formal power series with integer
coefficients. For $n,m\ge 1$ and $p$ prime, we show that $p^n+p^m\beta x+\alpha
x^2$ is reducible in $Z[[x]]$ if and only if it is reducible in $Z_p[x]$, the
ring of polynomials over the $p$-adic integers.


title:
Radiation reaction in the 2.5PN waveform from inspiralling binaries in
  circular orbits

abstract:
  In this Comment we compute the contributions of the radiation reaction force
in the 2.5 post-Newtonian (PN) gravitational wave polarizations for compact
binaries in circular orbits. (i) We point out and correct an inconsistency in
the derivation of Arun, Blanchet, Iyer, and Qusailah. (ii) We prove that all
contributions from radiation reaction in the 2.5PN waveform are actually
negligible since they can be absorbed into a modification of the orbital phase
at the 5PN order.


title: Luminous Red Galaxy Population in Clusters at $0.2\le z\le 0.6$

abstract:
  We investigate statistical properties of LRGs in a sample of X-ray selected
galaxy clusters at intermediate redshift ($0.2\le z\le0.6$). The LRGs are
selected based on carefully designed color criteria, and the cluster membership
is assessed via photometric redshifts. As clusters and LRGs are both viewed as
promising tracer of the underlying dark matter distribution, understanding the
distribution of LRGs within clusters is an important issue.
  Our main findings include:
  1. The halo occupation distribution of LRGs inside our cluster sample is
$N(M) = k\times (M/10^{14})^{a}$ where $a=0.620\pm 0.105 $ and $k=1.425\pm0.285
$ assuming a Poisson distribution for $N(M)$.
  2. The halo occupation distribution of LRGs ($N(M)$) and the satellite
distribution of LRGs ($N-1(M)$) are both consistent with being Poisson. To be
more quantitative, we find $Var(N)/<N>= 1.428\pm 0.351$ and $Var(N-1)/<N-1> =
1.823 \pm 0.496$
  3. The radial profile of LRGs within clusters when fitted with a NFW profile
gives a concentration of $17.5^{+7.1}_{-4.3}$ ($6.0^{+3.2}_{-1.9}$) including
(excluding) BLRGs (Brightest LRGs).
  We also discuss the implications of these observations on the evolution of
massive galaxies in clusters.


title: Inflationary de Sitter solutions from superstrings

abstract:
  In the framework of superstring compactifications with N=1 supersymmetry
spontaneously broken, (by either geometrical fluxes, branes or else), we show
the existence of new inflationary solutions. The time-trajectory of the scale
factor of the metric a, the supersymmetry breaking scale m=m(Phi) and the
temperature T are such that am and aT remain constant. These solutions request
the presence of special moduli-fields: i) The universal "no-scale-modulus" Phi,
which appears in all N=1 effective supergravity theories and defines the
supersymmetry breaking scale m(Phi). ii) The modulus Phi_s, which appears in a
very large class of string compactifications and has a Phi-dependent kinetic
term. During the time evolution, a^4 rho_s remains constant as well, (rho_s
being the energy density induced by the motion of Phi_s). The cosmological term
Lambda(am), the curvature term k(am, aT) and the radiation term c_R=a^4 rho are
dynamically generated in a controllable way by radiative and temperature
corrections; they are effectively constant during the time evolution. Depending
on Lambda, k and c_R, either a first or second order phase transition can occur
in the cosmological scenario. In the first case, an instantonic Euclidean
solution exists and connects via tunneling the inflationary evolution to
another cosmological branch. The latter starts with a big bang and, in the case
the transition does not occur, ends with a big crunch. In the second case, the
big bang and the inflationary phase are smoothly connected.


title: Resonance Production in RHIC Collisions

abstract:
  Results of resonance particle production measured at RHIC in $\sqrt{s_{\rm
NN}} = $ 200 GeV Au+Au collisions are compared to measurements in p+p and d+Au
collisions in order to verify the existence of an extended hardronically
interacting medium. Yield and momentum distributions of resonances maybe
modified during the fireball lifetime due to resonance decay and the subsequent
rescattering of their decay daughters as well as the regeneration of resonances
from their decay products. Modified momentum spectra in heavy ion collisions
may change the nuclear modification factor R$_{\rm AA}$. The influence on the
elliptic flow v$_{2}$ due to late regeneration of resonances is discussed.


title: Vibrational instability, two-level systems and Boson peak in glasses

abstract:
  We show that the same physical mechanism is fundamental for two seemingly
different phenomena such as the formation of two-level systems in glasses and
the Boson peak in the reduced density of low-frequency vibrational states
g(w)/w^2. This mechanism is the vibrational instability of weakly interacting
harmonic modes. Below some frequency w_c << w_0 (where w_0 is of the order of
Debye frequency) the instability, controlled by the anharmonicity, creates a
new stable universal spectrum of harmonic vibrations with a Boson peak feature
as well as double-well potentials with a wide distribution of barrier heights.
Both are determined by the strength of the interaction I ~ w_c between the
oscillators. Our theory predicts in a natural way a small value for the
important dimensionless parameter C ~ 10^{-4} for two-level systems in glasses.
We show that C ~ I^{-3} and decreases with increasing of the interaction
strength I. We show that the number of active two-level systems is very small,
less than one per ten million of oscillators, in a good agreement with
experiment. Within the unified approach developed in the present paper the
density of the tunneling states and the density of vibrational states at the
Boson peak frequency are interrelated.


title: On Semiclassical Limits of String States

abstract:
  We explore the relation between classical and quantum states in both open and
closed (super)strings discussing the relevance of coherent states as a
semiclassical approximation. For the closed string sector a gauge-fixing of the
residual world-sheet rigid translation symmetry of the light-cone gauge is
needed for the construction to be possible. The circular target-space loop
example is worked out explicitly.


title: Hot Jupiters in binary star systems

abstract:
  Radial velocity surveys find Jupiter mass planets with semi-major axes a less
than 0.1 AU around ~1% of solar-type stars; counting planets with $a$ as large
as 5 AU, the fraction of stars having planets reaches ~ 10% {Marcy,Butler}. An
examination of the distribution of semi-major axes shows that there is a clear
excess of planets with orbital periods around 3 or 4 days, corresponding to
a~0.03$ AU, with a sharp cutoff at shorter periods (see Figure 1). It is
believed that Jupiter mass planets form at large distances from their parent
stars; some fraction then migrate in to produce the short period objects. We
argue that a significant fraction of the `hot Jupiters' (a<0.1 AU) may arise in
binary star systems in which the orbit of the binary is highly inclined to the
orbit of the planet. Mutual torques between the two orbits drive down the
minimum separation or periapse r_p between the planet and its host star (the
Kozai mechanism). This periapse collapse is halted when tidal friction on the
planet circularizes the orbit faster than Kozai torque can excite it. The same
friction then circularizes the planet orbit, producing hot Jupiters with the
peak of the semimajor axis distribution lying around 3 days. For the observed
distributions of binary separation, eccentricity and mass ratio, roughly 2.5%
of planets with initial semimajor axis a_p ~ 5au will migrate to within 0.1au
of their parent star. Kozai migration could account for 10% or more of the
observed hot Jupiters.


title: Zero-range process with long-range interactions at a T-junction

abstract:
  A generalized zero-range process with a limited number of long-range
interactions is studied as an example of a transport process in which particles
at a T-junction make a choice of which branch to take based on traffic levels
on each branch. The system is analysed with a self-consistent mean-field
approximation which allows phase diagrams to be constructed. Agreement between
the analysis and simulations is found to be very good.


title: How Dry Are Red Mergers?

abstract:
  The focus of current research in galaxy evolution has increasingly turned to
understanding the effect that mergers have on the evolution of systems on the
red sequence. For those interactions purported to occur dissipationlessly (so
called "dry mergers"), it would appear that the role of gas is minimal.
However, if these mergers are not completely dry, then even low levels of gas
may be detectable. The purpose of our study is to test whether early type
galaxies with HI in or around them, or "wet" ellipticals, would have been
selected as dry mergers by the criteria in van Dokkum (2005, AJ, 130, 2647). To
that end, we examine a sample of 20 early types from the HI Rogues Gallery with
neutral hydrogen in their immediate environs. Of these, the 15 brightest and
reddest galaxies match the optical dry merger criteria, but in each case, the
presence of HI means that they are not truly dry.


title: Magnetoconductance of carbon nanotube p-n junctions

abstract:
  The magnetoconductance of p-n junctions formed in clean single wall carbon
nanotubes is studied in the noninteracting electron approximation and
perturbatively in electron-electron interaction, in the geometry where a
magnetic field is along the tube axis. For long junctions the low temperature
magnetoconductance is anomalously large: the relative change in the conductance
becomes of order unity even when the flux through the tube is much smaller than
the flux quantum. The magnetoconductance is negative for metallic tubes. For
semiconducting and small gap tubes the magnetoconductance is nonmonotonic;
positive at small and negative at large fields.


title:
Anisotropic low-temperature piezoresistance in (311)A GaAs
  two-dimensional holes

abstract:
  We report low-temperature resistance measurements in a modulation-doped,
(311)A GaAs two-dimensional hole system as a function of applied in-plane
strain. The data reveal a strong but anisotropic piezoresistance whose
magnitude depends on the density as well as the direction along which the
resistance is measured. At a density of $1.6\times10^{11}$ cm$^{-2}$ and for a
strain of about $2\times10^{-4}$ applied along [01$\bar{1}$], e.g., the
resistance measured along this direction changes by nearly a factor of two
while the resistance change in the [$\bar{2}$33] direction is less than 10% and
has the opposite sign. Our accurate energy band calculations indicate a
pronounced and anisotropic deformation of the heavy-hole dispersion with
strain, qualitatively consistent with the experimental data. The extremely
anisotropic magnitude of the piezoresistance, however, lacks a quantitative
explanation.


title:
Anomalous phonon behavior in the high temperature shape memory alloy:
  TiPd:Cr

abstract:
  Ti50 Pd50-xCrx is a high temperature shape memory alloy with a martensitic
transformation temperature strongly dependent on the Cr composition. Prior to
the transformation a premartensitic phase is present with an incommensurate
modulated cubic lattice with wave vector of q0=(0.22, 0.22, 0). The temperature
dependence of the diffuse scattering in the cubic phase is measured as a
function temperature for x=6.5, 8.5, and 10 at. %. The lattice dynamics has
been studied and reveals anomalous temperature and q-dependence of the
[110]-TA2 transverse phonon branch. The phonon linewidth is broad over the
entire Brillouin zone and increases with decreasing temperature, contrary to
the behavior expected for anharmonicity. No anomaly is observed at q0. The
results are compared with first principles calculation of the phonon structure.


title: A centimetre-wave excess over free-free emission in planetary nebulae

abstract:
  This paper has been withdrawn by the author(s), as it is superseded by
0708.2385.


title: Scaling Laws and Intermittency in Highly Compressible Turbulence

abstract:
  We use large-scale three-dimensional simulations of supersonic Euler
turbulence to study the physics of a highly compressible cascade. Our numerical
experiments describe non-magnetized driven turbulent flows with an isothermal
equation of state and an rms Mach number of 6. We find that the inertial range
velocity scaling deviates strongly from the incompressible Kolmogorov laws. We
propose an extension of Kolmogorov's K41 phenomenology that takes into account
compressibility by mixing the velocity and density statistics and preserves the
K41 scaling of the density-weighted velocity v=rho^{1/3}u. We show that
low-order statistics of 'v' are invariant with respect to changes in the Mach
number. For instance, at Mach 6 the slope of the power spectrum of 'v' is -1.69
and the third-order structure function of 'v' scales linearly with separation.
We directly measure the mass dimension of the "fractal" density distribution in
the inertial subrange, D_m=2.4, which is similar to the observed fractal
dimension of molecular clouds and agrees well with the cascade phenomenology.


title:
Reducing phase error in long numerical binary black hole evolutions with
  sixth order finite differencing

abstract:
  We describe a modification of a fourth-order accurate ``moving puncture''
evolution code, where by replacing spatial fourth-order accurate differencing
operators in the bulk of the grid by a specific choice of sixth-order accurate
stencils we gain significant improvements in accuracy. We illustrate the
performance of the modified algorithm with an equal-mass simulation covering
nine orbits.


title: On knot Floer homology in double branched covers

abstract:
  Let L be a link in an thickened annulus. We specify the embedding of this
annulus in the three sphere, and consider its complement thought of as the axis
to L. In the right circumstances this axis lifts to a null-homologous knot in
the double branched cover of the three sphere, branched over the embedded copy
of L. This paper shows that the knot Floer homology of this lift, with mod 2
coefficients, can be computed from a spectral sequence starting at a type of
Khovanov homology already described by Asaeda, Przytycki, and Sikora. We extend
the known results about this type of Khovanov homology, and use it to provide a
very simple explanation of the case when L is alternating for the obvious
projection.


title: Universal low-temperature behavior of the CePd_{1-x}Rh_x ferromagnet

abstract:
  The heavy-fermion metal CePd_{1-x}Rh_x evolves from ferromagnetism at x=0 to
a non-magnetic state at some critical concentration x_c. Utilizing the
quasiparticle picture and the concept of fermion condensation quantum phase
transition (FCQPT), we address the question about non-Fermi liquid (NFL)
behavior of ferromagnet CePd_{1-x}Rh_x and show that it coincides with that of
both antiferromagnet YbRh_2(Si_{0.95}Ge_{0.05})_2 and paramagnet CeRu_2Si_2 and
CeNi_2Ge_2. We conclude that the NFL behavior being independent of the
peculiarities of specific alloy, is universal, while numerous quantum critical
points assumed to be responsible for the NFL behavior of different HF metals
can be well reduced to the only quantum critical point related to FCQPT.


title: On knot Floer homology for some fibered knots

abstract:
  A companion paper to "On knot Floer homology in branched double covers"
applied to braided branched loci. We reprove the main result of that paper
concerning alternating branched loci when projected to an annulus, without
using Khovanov homology. This provides two advantages: 1) the results hold for
integer coefficients and 2) the spin^c structures are more readily discernable.
We apply this result to a branch locus which is a braid, and use the braid
structure to find information about a fibered knot in the branched double
cover. In some cases this provides all the information about the knot Floer
homology and can be used to derive information about the Heegaard-Floer
homology of associated fibered three manifolds. Results for certain positive
braids are also included, establishing results similar to E. Eftekhary's in the
Heegaard-Floer setting.


title: Free fermion resolution of supergroup WZNW models

abstract:
  Extending our earlier work on PSL(2|2), we explain how to reduce the solution
of WZNW models on general type I supergroups to those defined on the bosonic
subgroup. The new analysis covers in particular the supergroups GL(M|N) along
with several close relatives such as PSL(N|N), certain Poincare supergroups and
the series OSP(2|2N). This remarkable progress relies on the use of a special
Feigin-Fuchs type representation. In preparation for the field theory analysis,
we shall exploit a minisuperspace analogue of a free fermion construction to
deduce the spectrum of the Laplacian on type I supergroups. The latter is shown
to be non-diagonalizable. After lifting these results to the full WZNW model,
we address various issues of the field theory, including its modular invariance
and the computation of correlation functions. In agreement with previous
findings, supergroup WZNW models allow to study chiral and non-chiral aspects
of logarithmic conformal field theory within a geometric framework. We shall
briefly indicate how insights from WZNW models carry over to non-geometric
examples, such as e.g. the W(p) triplet models.

categories: hep-th cond-mat.stat-mech math-ph math.MP math.QA math.RT


title:
The zero-one law for planar random walks in i.i.d. random environments
  revisited

abstract:
  In this note we present a simplified proof of the zero-one law by Merkl and
Zerner (2001) for directional transience of random walks in i.i.d. random
environments (RWRE) on the square lattice. Also, we indicate how to construct a
two-dimensional counterexample in a non-uniformly elliptic and stationary
environment which has better ergodic properties than the example given by Merkl
and Zerner.


title: On the limited amplitude resolution of multipixel Geiger-mode APDs

abstract:
  The limited number of active pixels in a Geiger-mode Avalanche Photodiode
(G-APD) results not only in a non-linearity but also in an additional
fluctuation of its response. Both these effects are taken into account to
calculate the amplitude resolution of an ideal G-APD, which is shown to be
finite. As one of the consequences, the energy resolution of a scintillation
detector based on a G-APD is shown to be limited to some minimum value defined
by the number of pixels in the G-APD.


title:
Fast Adaptive Algorithms in the Non-Standard Form for Multidimensional
  Problems

abstract:
  We present a fast, adaptive multiresolution algorithm for applying integral
operators with a wide class of radially symmetric kernels in dimensions one,
two and three. This algorithm is made efficient by the use of separated
representations of the kernel. We discuss operators of the class
$(-\Delta+\mu^{2}I)^{-\alpha}$, where $\mu\geq0$ and $0<\alpha<3/2$, and
illustrate the algorithm for the Poisson and Schr\"{o}dinger equations in
dimension three. The same algorithm may be used for all operators with radially
symmetric kernels approximated as a weighted sum of Gaussians, making it
applicable across multiple fields by reusing a single implementation.
  This fast algorithm provides controllable accuracy at a reasonable cost,
comparable to that of the Fast Multipole Method (FMM). It differs from the FMM
by the type of approximation used to represent kernels and has an advantage of
being easily extendable to higher dimensions.


title:
On the lower bound of the spectral norm of symmetric random matrices
  with independent entries

abstract:
  We show that the spectral radius of an $N\times N$ random symmetric matrix
with i.i.d. bounded centered but non-symmetrically distributed entries is
bounded from below by $ 2 \*\sigma - o(N^{-6/11+\epsilon}), $ where $\sigma^2 $
is the variance of the matrix entries and $\epsilon $ is an arbitrary small
positive number. Combining with our previous result from [7], this proves that
for any $\epsilon >0, $ one has $$ \|A_N\| =2 \*\sigma + o(N^{-6/11+\epsilon})
$$ with probability going to 1 as $N \to \infty. $


title:
Peculiar Ferrimagnetism Associated with Charge Order in Layered
  Perovskite GdBaMn2O5

abstract:
  The magnetic properties of GdBaMn_{2}O_{5.0}, which exhibits charge ordering,
are studied from 2 to 400 K using single crystals. In a small magnetic field
applied along the easy axis, the magnetization M shows a temperature-induced
reversal which is sometimes found in ferrimagnets. In a large magnetic field,
on the other hand, a sharp change in the slope of M(T) coming from an unusual
turnabout of the magnetization of the Mn sublattices is observed. Those
observations are essentially explained by a molecular field theory which
highlights the role of delicate magnetic interactions between Gd^{3+} ions and
the antiferromagnetically coupled Mn^{2+}/Mn^{3+} sublattices.


title: An analogue of Szego's limit theorem in free probability theory

abstract:
  In the paper, we discuss orthogonal polynomials in free probability theory.
Especially, we prove an analogue of of Szego's limit theorem in free
probability theory.


title: Log canonical thresholds of certain Fano hypersurfaces

abstract:
  We study log canonical thresholds on quartic threefolds, quintic fourfolds,
and double spaces. As an application, we show that they have a Kaehler-Einstein
metric if they are general.


title:
Coronal ion-cyclotron beam instabilities within the multi-fluid
  description

abstract:
  Spectroscopic observations and theoretical models suggest resonant
wave-particle interactions, involving high-frequency ion-cyclotron waves, as
the principal mechanism for heating and accelerating ions in the open coronal
holes. However, the mechanism responsible for the generation of the
ion-cyclotron waves remains unclear. One possible scenario is that ion beams
originating from small-scale reconnection events can drive micro-instabilities
that constitute a possible source for the excitation of ion-cyclotron waves. In
order to study ion beam-driven electromagnetic instabilities, the multi-fluid
model in the low-beta coronal plasma is used. While neglecting the electron
inertia this model allows one to take into account ion-cyclotron wave effects
that are absent from the one-fluid MHD model. Realistic models of density and
temperature as well as a 2-D analytical magnetic field model are used to define
the background plasma in the open-field funnel region of a polar coronal hole.
Considering the WKB approximation, a Fourier plane-wave linear mode analysis is
employed in order to derive the dispersion relation. Ray-tracing theory is used
to compute the ray path of the unstable wave as well as the evolution of the
growth rate of the wave while propagating in the coronal funnel. We demonstrate
that, in typical coronal holes conditions and assuming realistic values of the
beam velocity, the free energy provided by the ion beam propagating parallel
the ambient field can drive micro-instabilities through resonant ion-cyclotron
excitation.


title:
Statistical Mechanics of Time Independent Non-Dissipative Nonequilibrium
  States

abstract:
  We examine the question of whether the formal expressions of equilibrium
statistical mechanics can be applied to time independent non-dissipative
systems that are not in true thermodynamic equilibrium and are nonergodic. By
assuming the phase space may be divided into time independent, locally ergodic
domains, we argue that within such domains the relative probabilities of
microstates are given by the standard Boltzmann weights. In contrast to
previous energy landscape treatments, that have been developed specifically for
the glass transition, we do not impose an a priori knowledge of the
inter-domain population distribution. Assuming that these domains are robust
with respect to small changes in thermodynamic state variables we derive a
variety of fluctuation formulae for these systems. We verify our theoretical
results using molecular dynamics simulations on a model glass forming system.
Non-equilibrium Transient Fluctuation Relations are derived for the
fluctuations resulting from a sudden finite change to the system's temperature
or pressure and these are shown to be consistent with the simulation results.
The necessary and sufficient conditions for these relations to be valid are
that the domains are internally populated by Boltzmann statistics and that the
domains are robust. The Transient Fluctuation Relations thus provide an
independent quantitative justification for the assumptions used in our
statistical mechanical treatment of these systems.


title: Metal Cooling in Simulations of Cosmic Structure Formation

abstract:
  The addition of metals to any gas can significantly alter its evolution by
increasing the rate of radiative cooling. In star-forming environments,
enhanced cooling can potentially lead to fragmentation and the formation of
low-mass stars, where metal-free gas-clouds have been shown not to fragment.
Adding metal cooling to numerical simulations has traditionally required a
choice between speed and accuracy. We introduce a method that uses the
sophisticated chemical network of the photoionization software, Cloudy, to
include radiative cooling from a complete set of metals up to atomic number 30
(Zn) that can be used with large-scale three-dimensional hydrodynamic
simulations. Our method is valid over an extremely large temperature range (10
K < T < 10^8 K), up to hydrogen number densities of 10^12 cm^-3. At this
density, a sphere of 1 Msun has a radius of roughly 40 AU. We implement our
method in the adaptive mesh refinement (AMR) hydrodynamic/N-body code, Enzo.
Using cooling rates generated with this method, we study the physical
conditions that led to the transition from Population III to Population II star
formation. While C, O, Fe, and Si have been previously shown to make the
strongest contribution to the cooling in low-metallicity gas, we find that up
to 40% of the metal cooling comes from fine-structure emission by S, when solar
abundance patterns are present. At metallicities, Z > 10^-4 Zsun, regions of
density and temperature exist where gas is both thermally unstable and has a
cooling time less than its dynamical time. We identify these doubly unstable
regions as the most inducive to fragmentation. At high redshifts, the CMB
inhibits efficient cooling at low temperatures and, thus, reduces the size of
the doubly unstable regions, making fragmentation more difficult.


title: The Calibration and Data Products of the Galaxy Evolution Explorer

abstract:
  We describe the calibration status and data products pertaining to the GR2
and GR3 data releases of the Galaxy Evolution Explorer (GALEX). These releases
have identical pipeline calibrations that are significantly improved over the
GR1 data release. GALEX continues to survey the sky in the Far Ultraviolet
(FUV, ~154 nm) and Near Ultraviolet (NUV, ~232 nm) bands, providing
simultaneous imaging with a pair of photon counting, microchannel plate, delay
line readout detectors. These 1.25 degree field-of-view detectors are
well-suited to ultraviolet observations because of their excellent red
rejection and negligible background. A dithered mode of observing and photon
list output pose complex requirements on the data processing pipeline,
entangling detector calibrations and aspect reconstruction algorithms. Recent
improvements have achieved photometric repeatability of 0.05 and 0.03 mAB in
the FUV and NUV, respectively. We have detected a long term drift of order 1%
FUV and 6% NUV over the mission. Astrometric precision is of order 0.5" RMS in
both bands. In this paper we provide the GALEX user with a broad overview of
the calibration issues likely to be confronted in the current release.
Improvements are likely as the GALEX mission continues into an extended phase
with a healthy instrument, no consumables, and increased opportunities for
guest investigations.


title:
Boundedness of projection operators and Ces\`aro means in weighted $L^p$
  space on the unit sphere

abstract:
  For the weight function $\prod_{i=1}^{d+1}|x_i|^{2\k_i}$ on the unit sphere,
sharp local estimates of the orthogonal projection operators are obtained and
used to prove the convergence of the Ces\`aro $(C,\delta)$ means in the
weighted $L^p$ space for $\delta$ below the critical index. Similar results are
also proved for corresponding weight functions on the unit ball and on the
simplex.


title: Fractional Quantum Hall Effect in Optical Lattices

abstract:
  We analyze a recently proposed method to create fractional quantum Hall (FQH)
states of atoms confined in optical lattices [A. S{\o}rensen {\it et al.},
Phys. Rev. Lett. {\bf 94} 086803 (2005)]. Extending the previous work, we
investigate conditions under which the FQH effect can be achieved for bosons on
a lattice with an effective magnetic field and finite onsite interaction.
Furthermore, we characterize the ground state in such systems by calculating
Chern numbers which can provide direct signatures of topological order and
explore regimes where the characterization in terms of wavefunction overlap
fails. We also discuss various issues which are relevant for the practical
realization of such FQH states with ultracold atoms in an optical lattice,
including the presence of the long-range dipole interaction which can improve
the energy gap and stabilize the ground state. We also investigate a new
detection technique based on Bragg spectroscopy to probe these system in an
experimental realization.


title:
Long time existence of smooth solutions for the rapidly rotating
  shallow-water and Euler equations

abstract:
  We study the stabilizing effect of rotational forcing in the nonlinear
setting of two-dimensional shallow-water and more general models of
compressible Euler equations. In [H. Liu and E. Tadmor, Phys. D 188 (2004), no.
3-4, 262-276] we have shown that the pressureless version of these equations
admit global smooth solution for a large set of sub-critical initial
configurations. In the present work we prove that when rotational force
dominates the pressure, it \emph{prolongs} the life-span of smooth solutions
for t < ln(1/d); here d << 1 is the ratio of the pressure gradient measured by
the inverse squared Froude number, relative to the dominant rotational forces
measured by the inverse Rossby number. Our study reveals a ``nearby''
periodic-in-time approximate solution in the small d-regime, upon which hinges
the long time existence of the exact smooth solution. These results are in
agreement with the close-to periodic dynamics observed in the ``near inertial
oscillation'' (NIO) regime which follows oceanic storms. Indeed, our results
indicate the existence of smooth, ``approximate periodic'' solution for a time
period of \emph{days}, which is the relevant time period found in NIO
obesrvations.


title:
Vortex Lattice Structures of a Bose-Einstein Condensate in a Rotating
  Triangular Lattice Potential

abstract:
  We study the vortex pinning effect in a Bose-Einstein Condensate in the
presence of a rotating lattice potential by numerically solving the
time-dependent Gross-Pitaevskii equation. We consider a triangular lattice
potential created by blue-detuned laser beams. By rotating the lattice
potential, we observe a transition from the Abrikosov vortex lattice to the
pinned vortex lattice. We investigate the transition of the vortex lattice
structure by changing conditions such as angular velocity, strength, and
lattice constant of a rotating lattice potential. Our simulation results
clearly show that the lattice potential has a strong vortex pinning effect when
the vortex density coincides with the density of the pinning points.


title: Neutral Networks of Sequence to Shape Maps

abstract:
  In this paper we present a novel framework for sequence to shape maps. These
combinatorial maps realize exponentially many shapes, and have preimages which
contain extended connected subgraphs of diameter n (neutral networks). We prove
that all basic properties of RNA folding maps also hold for combinatorial maps.
Our construction is as follows: suppose we are given a graph $H$ over the $\{1
>...,n\}$ and an alphabet of nucleotides together with a symmetric relation
$\mathcal{R}$, implied by base pairing rules. Then the shape of a sequence of
length n is the maximal H subgraph in which all pairs of nucleotides incident
to H-edges satisfy $\mathcal{R}$. Our main result is to prove the existence of
at least $\sqrt{2}^{n-1}$ shapes with extended neutral networks, i.e. shapes
that have a preimage with diameter $n$ and a connected component of size at
least $(\frac{1+\sqrt{5}}{2})^n+(\frac{1-\sqrt{5}}{2})^n$. Furthermore, we show
that there exists a certain subset of shapes which carries a natural graph
structure. In this graph any two shapes are connected by a path of shapes with
respective neutral networks of distance one. We finally discuss our results and
provide a comparison with RNA folding maps.

categories: q-bio.QM math-ph math.CO math.MP q-bio.BM


title: Myriad phases of the Checkerboard Hubbard Model

abstract:
  The zero temperature phase diagram of the checkerboard Hubbard model is
obtained in the solvable limit in which it consists of weakly coupled square
plaquettes. As a function of the on-site Coulomb repulsion U and the density of
holes per site, x, we demonstrate the existence of at least 16 distinct phases.
For instance, at zero doping, the ground state is a novel d-wave Mott insulator
(d-Mott), which is not adiabatically continuable to a band insulator; by doping
the d-Mott state with holes, depending on the magnitude of U, it gives way to a
d-wave superconducting state, a two-flavor spin-1/2 Fermi liquid (FL), or a
spin-3/2 FL.


title: Propagating modes of non-Abelian tensor gauge field of second rank

abstract:
  In the recently proposed extension of the YM theory, non-Abelian tensor gauge
field of the second rank is represented by a general tensor whose symmetric
part describes the propagation of charged gauge boson of helicity two and its
antisymmetric part - the helicity zero charged gauge boson. On the
non-interacting level these polarizations are similar to the polarizations of
the graviton and of the Abelian antisymmetric B field, but the interaction of
these gauge bosons carrying non-commutative internal charges cannot be directly
identified with the interaction of gravitons or B field. Our intention here is
to illustrate this result from different perspectives which would include
Bianchi identity for the corresponding field strength tensor and the analysis
of the second-order partial differential equation which describes in this
theory the propagation of non-Abelian tensor gauge field of the second rank.


title: Jet-Driven Disk Accretion in Low Luminosity AGN?

abstract:
  We explore an accretion model for low luminosity AGN (LLAGN) that attributes
the low radiative output to a low mass accretion rate rather than a low
radiative efficiency. In this model, electrons are assumed to drain energy from
the ions as a result of collisionless plasma microinstabilities. Consequently,
the accreting gas collapses to form a geometrically thin disk at small radii
and is able to cool before reaching the black hole. The accretion disk is not a
standard disk, however, because the radial disk structure is modified by a
magnetic torque which drives a jet and which is primarily responsible for
angular momentum transport. We also include relativistic effects. We apply this
model to the well known LLAGN M87 and calculate the combined disk-jet
steady-state broadband spectrum. A comparison between predicted and observed
spectra indicates that M87 may be a maximally spinning black hole accreting at
a rate of 10^{-3} solar masses per year. This is about 6 orders of magnitude
below the Eddington rate for the same radiative efficiency. Furthermore, the
total jet power inferred by our model is in remarkably good agreement with the
value independently deduced from observations of the M87 jet on kiloparsec
scales.


title:
Pattern Selection in the Complex Ginzburg-Landau Equation with
  Multi-Resonant Forcing

abstract:
  We study the excitation of spatial patterns by resonant, multi-frequency
forcing in systems undergoing a Hopf bifurcation to spatially homogeneous
oscillations. Using weakly nonlinear analysis we show that for small amplitudes
only stripe or hexagon patterns are linearly stable, whereas square patterns
and patterns involving more than three modes are unstable. In the case of
hexagon patterns up- and down-hexagons can be simultaneously stable. The
third-order, weakly nonlinear analysis predicts stable square patterns and
super-hexagons for larger amplitudes. Direct simulations show, however, that in
this regime the third-order weakly nonlinear analysis is insufficient, and
these patterns are, in fact unstable.


title:
Measuring the Decoherence of a Quantronium Qubit with the Cavity
  Bifurcation Amplifier

abstract:
  Dispersive readouts for superconducting qubits have the advantage of speed
and minimal invasiveness. We have developed such an amplifier, the Cavity
Bifurcation Amplifier (CBA) [10], and applied it to the readout of the
quantronium qubit [2]. It consists of a Josephson junction embedded in a
microwave on-chip resonator. In contrast with the Josephson bifurcation
amplifier [17], which has an on-chip capacitor shunting a junction, the
resonator is based on a simple coplanar waveguide imposing a pre-determined
frequency and whose other RF characteristics like the quality factor are easily
controlled and optimized. Under proper microwave irradiation conditions, the
CBA has two metastable states. Which state is adopted by the CBA depends on the
state of a quantronium qubit coupled to the CBA's junction. Due to the MHz
repetition rate and large signal to noise ratio we can show directly that the
coherence is limited by 1/f gate charge noise when biased at the sweet spot - a
point insensitive to first order gate charge fluctuations. This architecture
lends itself to scalable quantum computing using a multi-resonator chip with
multiplexed readouts.


title:
$^1$H-NMR Study of the Random Bond Effect in the Quantum Spin System
  (CH$_3$)$_2$CHNH$_3$Cu(Cl$_x$Br$_{1-x}$)$_3$

abstract:
  Spin-lattice relaxation rate $T_1^{-1}$ of $^1$H-NMR has been measured in
(CH$_3$)$_2$CHNH$_3$Cu(Cl$_x$Br$_{1-x}$)$_3$ with $x=0.88$, which has been
reported to be gapped system with singlet ground state from the previous
macroscopic magnetization and specific heat measurements, in order to
investigate the bond randomness effect microscopically in the gapped composite
Haldane system (CH$_3$)$_2$CHNH$_3$CuCl$_3$. It was found that the spin-lattice
relaxation rate $T_1^{-1}$ in the present system includes both fast and slow
relaxation parts indicative of the gapless magnetic ground state and the gapped
singlet ground state, respectively. We discuss the obtained results with the
previous macroscopic magnetization and specific heat measurements together with
the microscopic $\mu$SR experiments.


title: Skew-orthogonal polynomials: the quartic case

abstract:
  We present an iterative technique to obtain skew-orthogonal polynomials with
quartic weight, arising in the study of symplectic ensembles of random
matrices.


title: Exact Heisenberg operator solutions for multi-particle quantum mechanics

abstract:
  Exact Heisenberg operator solutions for independent `sinusoidal coordinates'
as many as the degree of freedom are derived for typical exactly solvable
multi-particle quantum mechanical systems, the Calogero systems based on any
root system. These Heisenberg operator solutions also present the explicit
forms of the annihilation-creation operators for various quanta in the
interacting multi-particle systems. At the same time they can be interpreted as
multi-variable generalisation of the three term recursion relations for
multi-variable orthogonal polynomials constituting the eigenfunctions.

categories: quant-ph cond-mat.other hep-th math-ph math.CA math.MP nlin.SI


title: Characterization of topological states on a lattice with Chern number

abstract:
  We study Chern numbers to characterize the ground state of strongly
interacting systems on a lattice. This method allows us to perform a numerical
characterization of bosonic fractional quantum Hall (FQH) states on a lattice
where conventional overlap calculation with known continuum case such as
Laughlin state, breaks down due to the lattice structure or dipole-dipole
interaction. The non-vanishing Chern number indicates the existence of a
topological order in the degenerate ground state manifold.


title: High Resolution X-Ray Imaging of the Center of IC342

abstract:
  We presented the result of a high resolution (FWHM~0.5'') 12 ks Chandra HRC-I
observation of the starburst galaxy IC342 taken on 2 April 2006. We identified
23 X-ray sources within the central 30' x 30' region of IC342. Our HRC-I
observation resolved the historical Ultraluminous X-ray sources (ULX), X3, near
the nucleus into 2 sources, namely C12 and C13, for the first time. The
brighter source C12, with L(0.08-10keV)=(6.66\pm0.45)\times10^{38}ergs^-1, was
spatially extended (~82 pc x 127 pc). From the astrometric registration of the
X-ray image, C12 was at R.A.=03h:46m:48.43s, decl.=+68d05m47.45s, and was
closer to the nucleus than C13. Thus we concluded that source was not an ULX
and must instead be associated with the nucleus. The fainter source C13, with
L(0.08-10keV)=(5.1\pm1.4) x 10^{37}ergs^-1 was consistent with a point source
and located $6.51'' at P.A. 240 degree of C12.
  We also analyzed astrometrically corrected optical Hubble Space Telescope and
radio Very Large Array images, a comparison with the X-ray image showed
similarities in their morphologies. Regions of star formation within the
central region of IC342 were clearly visible in HST H alpha image and this was
the region where 3 optical star clusters and correspondingly our detected X-ray
source C12 were observed. We found that a predicted X-ray emission from
starburst was very close to the observed X-ray luminosity of C12, suggesting
that nuclear X-ray emission in IC342 was dominated by starburst. Furthermore,
we discussed the possibility of AGN in the nucleus of IC342. Although our data
was not enough to give a firm existence of an AGN, it could not be discarded.


title: Fully nonlinear excitations of non-Abelian plasma

abstract:
  We investigate fully nonlinear, non-Abelian excitations of quark-antiquark
plasma, using relativistic fluid theory in cold plasma approximation. There are
mainly three important nonlinearities, coming from various sources such as
non-Abelian interactions of Yang-Mills (YM) fields, Wong's color dynamics and
plasma nonlinearity, in our model. By neglecting nonlinearities due to plasma
and color dynamics we get back the earlier results of Blaizot {\it et. al.},
Phys. Rev. Lett. 72, 3317 (1994). Similarly, by neglecting YM fields
nonlinearity and plasma nonlinearity, it reduces to the model of Gupta {\it et.
al.}, Phys. Lett. B498, 223 (2005). Thus we have the most general non-Abelian
mode of quark-gluon plasma (QGP). Further, our model resembles the problem of
propagation of laser beam through relativistic plasma, Physica 9D, 96 (1983).
in the absence of all non-Abelian interactions.


title:
Multiple reference states and complete spectrum of the $Z_n$ Belavin
  model with open boundaries

abstract:
  The multiple reference state structure of the $\Z_n$ Belavin model with
non-diagonal boundary terms is discovered. It is found that there exist $n$
reference states, each of them yields a set of eigenvalues and Bethe Ansatz
equations of the transfer matrix. These $n$ sets of eigenvalues together
constitute the complete spectrum of the model. In the quasi-classic limit, they
give the complete spectrum of the corresponding Gaudin model.


title:
Interband, intraband and excited-state direct photon absorption of
  silicon and germanium nanocrystals embedded in a wide band-gap lattice

abstract:
  Embedded Si and Ge nanocrystals (NCs) in wide band-gap matrices are studied
theoretically using an atomistic pseudopotential approach. From small clusters
to large NCs containing on the order of several thousand atoms are considered.
Effective band-gap values as a function of NC diameter reproduce very well the
available experimental and theoretical data. It is observed that the highest
occupied molecular orbital for both Si and Ge NCs and the lowest unoccupied
molecular orbital for Si NCs display oscillations with respect to size among
the different irreducible representations of the $C_{3v}$ point group to which
these spherical NCs belong. Based on this electronic structure, first the
interband absorption is thoroughly studied which shows the importance of
surface polarization effects that significantly reduce the absorption when
included. This reduction is found to increase with decreasing NC size or with
increasing permittivity mismatch between the NC core and the host matrix.
Reasonable agreement is observed with the experimental absorption spectra where
available. The deformation of spherical NCs into prolate or oblate ellipsoids
are seen to introduce no pronounced effects for the absorption spectra. Next,
intraconduction and intravalence band absorption coefficients are obtained in
the wavelength range from far-infrared to visible region. These results can be
valuable for the infrared photodetection prospects of these NC arrays. Finally,
excited-state absorption at three different optical pump wavelengths, 532 nm,
355 nm and 266 nm are studied for 3- and 4 nm-diameter NCs. This reveals strong
absorption windows in the case of holes and a broad spectrum in the case of
electrons which can especially be relevant for the discussions on achieving
gain in these structures.


title: Segregation and Stability of Binary Granular Mixtures

abstract:
  We measure stability of two-dimensional granular mixtures in a rotating drum
and relate grain configurations to stability. For our system, the smaller but
smoother grains cluster near the center of the drum, while the larger, rougher
grains remain near the outer edge. One consequence of the size segregation is
that the smaller grains heavily influence the stability of the heap. We find
that the maximum angle of stability is a non-linear function of composition,
changing particularly rapidly when small grains are first added to a
homogeneous pile of large grains. We conclude that the grain configuration
within the central portion of the heap plays a prominent role in stability.


title: Raman Spectroscopy of Nanostructures and Nanosized Materials

abstract:
  The interest of micro and tip-enhanced Raman spectroscopy to analyze
nanosized and nanostructured materials, chiefly semiconductors, oxides and
pristine or functionalized carbon nanotubes, is reviewed at the light of the
contributions to this special issue. Particular attention is paid to the fact
that chemical reactions, size or shape distribution, defects, strain and
couplings may add to nano-dimensionality in defining the Raman signature.


title:
Nanomechanics of single keratin fibres: A Raman study of the alpha helix
  -> beta sheet transition and water effect

abstract:
  The use of micro-Raman spectroscopy, through chemical bond nano-scale probes,
allows the changes in conformations (alpha helix -> beta sheet), chain
orientation, disconnection of disulfide bonds (-20%) and the increase of intra
and inter-chain distances during the strain to be distinguished. The
combination of micro-Raman spectroscopy and a allows a quantitative measure of
the extension of chemical bonds in the peptidic chain during loading. The
nano-structural transformations of keratin during the strain of human hair in a
dry environment (40-60 % relative humidity) and saturated with water have been
studied. The water permits the sliding of the chains and decreases the bond
energy hair. Spectral analyses and 2D correlation are two coherent and
independent methods to follow change the Raman probes which are sensitive to
structural . The between nano-mechanical (Raman) and micro-mechanical
(strain/stress) analyses confirms the validity of the experimental results,
tools and principles used, as well as the agreement with the structural model
of keratin fibres described by Chapman & Hearle.


title: Bound States and Many-Body Effects in H-Shaped Quantum Wires

abstract:
  In this paper, bound states energies and corresponding wave functions of
H-shaped quantum wires are calculated numerically in the presence of external
magnetic and electric fields and within the Landau gauge. With a suitable
definition of external confinement potential, we present a numerical algorithm
to calculate the profile of probability distribution of charge carriers. Our
analysis shows that in the presence of external electric and magnetic fields,
bound state properties of carriers are sensitive functions of an asymmetric
parameter $a=\frac{W_{x}}{W_{y}}$ which measures the relative width of the well
in two directions. We also study many body effect of bandgap renormalization in
this quasi one dimensional system within dynamical random phase approximation.


title:
Nodeless Superconductivity in the Noncentrosymmetric Superconductor
  $Mg_{10}Ir_{19}B_{16}$

abstract:
  We measured the resistivity, diamagnetization and low temperature specific
heat of the newly discovered noncentrosymmetric superconductor
$Mg_{10}Ir_{19}B_{16}$. It is found that the superconducting gap has an s-wave
symmetry with a value of about $\Delta_0 \approx$ 0.6 meV, and the ratio
$\Delta_0/k_BT_c\approx1.86$ indicates a weak coupling for the
superconductivity. The correlations among the normal state Sommerfeld constant
$\gamma_n$, the slope $-d\mu_0H_{c2}(T)/dT$ near Tc and the condensation energy
Ec are all consistent with the weak coupling picture. The separated phonon
contribution from the specific heat shows that the conduction electrons of the
$Ir$ atoms interact most strongly with the vibrations of themselves, instead of
with that of the light element boron.


title:
General theory of electromagnetic fluctuations near a homogeneous
  surface, in terms of its reflection amplitudes

abstract:
  We derive new general expressions for the fluctuating electromagnetic field
outside a homogeneous material surface. The analysis is based on general
results from the thermodynamics of irreversible processes, and requires no
consideration of the material interior, as it only uses knowledge of the
reflection amplitudes for its surface. Therefore, our results are valid for all
homogeneous surfaces, including layered systems and metamaterials, at all
temperatures. In particular, we obtain new formulae for the near-field region,
which are important for interpreting the numerous current experiments probing
proximity effects for macroscopic and/or microscopic bodies separated by small
empty gaps. By use of Onsager's reciprocity relations, we obtain also the
general symmetry properties that must be satisfied by the reflection matrix of
any material.


title: Planar Vacuum Diode With Monoenergetic Electrons

abstract:
  The paper analyses volt-ampere characteristics of a planar vacuum diode with
mono-energetic electrons, emitted by the cathode (an electron beam). The
movement of the electron beam in the volume of the diode is described. An
analytic dependence of the volt-ampere characteristics in an unlimited and
limited by the field mode of the electron beam is derived.


title: Two-loop SUSY QCD corrections to the chargino masses in the MSSM

abstract:
  We have calculated the two-loop strong interaction corrections to the
chargino pole masses in the DRbar'-scheme in the Minimal Supersymmetric
Standard Model (MSSM) with complex parameters. We have performed a detailed
numerical analysis for a particular point in the parameter space and found
corrections of a few tenths of a percent. We provide a computer program which
calculates chargino and neutralino masses with complex parameters including the
one-loop corrections and all two-loop SQCD effects.


title: D-dualized D-brane

abstract:
  We further investigate the dimensional duality (D-duality) proposed in
arXiv:0705.0550 by mainly focusing on the properties of D-branes in this
background. We derive the world-sheet correspondence of static D-branes, and
discuss the fate of non-static D-branes from the world-sheet viewpoint. The
quantum string production with or without D-branes is also studied from the
time-like Liouville theory. We find that the closed string production from the
background is much larger than that from D-branes decaying into nothing.


title:
A Huge Filamentary Structure at z=0.55 and Star Formation Histories of
  Galaxies at z<1

abstract:
  We report a definitive confirmation of a large-scale structure around the
super rich cluster CL0016+1609 at z=0.55. We made spectroscopic follow-up
observations with FOCAS on Subaru along the large filamentary structure
identified in our previous photometric studies. We have confirmed the physical
connection of the huge filament extending over 20 Mpc in the N-S direction, and
another filament extending from the main cluster to the East. Based on a simple
energy argument, we show that it is likely that most of the clumps are bound to
the main CL0016 cluster. This structure is surely one of the most prominent
confirmed structures ever identified in the distant Universe, which then serves
as an ideal laboratory to examine the environmental variation of galaxy
properties. We draw star formation histories of galaxies from the composite
spectra of red galaxies in field, group, and cluster environments. Combining
the results from our previous studies, we find that red galaxies in groups at
z~0.8 and red field galaxies at z~0.5 show strong Hd absorption lines for their
D4000 indices. These are the environments in which we observed the on-going
build-up of the colour-magnitude relation in our previous photometric analyses.
The strong Hd absorption lines imply that their star formation is truncated on
a relatively short time scale. We suggest that a galaxy-galaxy interaction is
the most likely physical driver of the truncation of star formation and thus
responsible for the build-up of the colour-magnitude relation since z~1.
(Abridged)


title: Space Velocities of L- and T-type Dwarfs

abstract:
  (Abridged) We have obtained radial velocities of a sample of 18 ultracool
dwarfs (M6.5-T8) using high-resolution, near-infrared spectra obtained with
NIRSPEC and the Keck II telescope. We have confirmed that the radial velocity
of Gl 570 D is coincident with that of the K-type primary star Gl 570 A, thus
providing additional support for their true companionship. The presence of
planetary-mass companions around 2MASS J05591914-1404488 (T4.5V) has been
analyzed using five NIRSPEC radial velocity measurements obtained over a period
of 4.37 yr. We have computed UVW space motions for a total of 21 L and T dwarfs
within 20 pc of the Sun. This population shows UVW velocities that nicely
overlap the typical kinematics of solar to M-type stars within the same spatial
volume. However, the mean Galactic (44.2 km/s) and tangential (36.5 km/s)
velocities of the L and T dwarfs appear to be smaller than those of G to M
stars. A significant fraction (~40%) of the L and T dwarfs lies near the Hyades
moving group (0.4-2 Gyr), which contrasts with the 10-12% found for
earlier-type stellar neighbors. Additionally, the distributions of all three
UVW components (sigma_{UVW} = 30.2, 16.5, 15.8 km/s) and the distributions of
the total Galactic (sigma_{v_tot} = 19.1 km/s) and tangential (sigma_{v_t} =
17.6 km/s) velocities derived for the L and T dwarf sample are narrower than
those measured for nearby G, K, and M-type stars, but similar to the
dispersions obtained for F stars. This suggests that, in the solar
neighborhood, the L- and T-type ultracool dwarfs in our sample (including brown
dwarfs) is kinematically younger than solar-type to early M stars with likely
ages in the interval 0.5-4 Gyr.


title: How to compose Lagrangian?

abstract:
  A method for constructing Lagrangians for the Lie transformation groups is
explained. As examples, the Lagrangians for real plane rotations and affine
transformations of the real line are constructed.


title: A Conjecture on Primes and a Step towards Justification

abstract:
  We put a new conjecture on primes from the point of view of its binary
expansions and make a step towards justification.


title:
Construction of Bayesian Deformable Models via Stochastic Approximation
  Algorithm: A Convergence Study

abstract:
  The problem of the definition and the estimation of generative models based
on deformable templates from raw data is of particular importance for modelling
non aligned data affected by various types of geometrical variability. This is
especially true in shape modelling in the computer vision community or in
probabilistic atlas building for Computational Anatomy (CA). A first coherent
statistical framework modelling the geometrical variability as hidden variables
has been given by Allassonni\`ere, Amit and Trouv\'e (JRSS 2006). Setting the
problem in a Bayesian context they proved the consistency of the MAP estimator
and provided a simple iterative deterministic algorithm with an EM flavour
leading to some reasonable approximations of the MAP estimator under low noise
conditions. In this paper we present a stochastic algorithm for approximating
the MAP estimator in the spirit of the SAEM algorithm. We prove its convergence
to a critical point of the observed likelihood with an illustration on images
of handwritten digits.


title: Polynomial maps that are roots of power series

abstract:
  We introduce a class of polynomial maps that we call polynomial roots of
powerseries, and show that automorphisms with this property generate the
automorphism group in any dimension. In particular we determine generically
which polynomial maps that preserve the origin are roots of powerseries. We
study the one-dimensional case in greater depth.


title: Limit laws for k-coverage of paths by a Markov-Poisson-Boolean model

abstract:
  Let P := {X_i,i >= 1} be a stationary Poisson point process in R^d, {C_i,i >=
1} be a sequence of i.i.d. random sets in R^d, and {Y_i^t; t \geq 0, i >= 1} be
i.i.d. {0,1}-valued continuous time stationary Markov chains. We define the
Markov-Poisson-Boolean model C_t := {Y_i^t(X_i + C_i), i >= 1}. C_t represents
the coverage process at time t. We first obtain limit laws for k-coverage of an
area at an arbitrary instant. We then obtain the limit laws for the k-coverage
seen by a particle as it moves along a one-dimensional path.


title: Free Actions of Finite Groups on $S^n \times S^n$

abstract:
  Let $p$ be an odd prime. We construct a non-abelian extension $\Gamma$ of
$S^1$ by $Z/p \times Z/p$, and prove that any finite subgroup of $\Gamma$ acts
freely and smoothly on $S^{2p-1} \times S^{2p-1}$. In particular, for each odd
prime $p$ we obtain free smooth actions of infinitely many non-metacyclic rank
two $p$-groups on $S^{2p-1} \times S^{2p-1}$. These results arise from a
general approach to the existence problem for finite group actions on products
of equidimensional spheres.


title:
A volume inequality for quantum Fisher information and the uncertainty
  principle

abstract:
  Let $A_1,...,A_N$ be complex self-adjoint matrices and let $\rho$ be a
density matrix. The Robertson uncertainty principle $$ det(Cov_\rho(A_h,A_j))
\geq det(- \frac{i}{2} Tr(\rho [A_h,A_j])) $$ gives a bound for the quantum
generalized covariance in terms of the commutators $[A_h,A_j]$. The right side
matrix is antisymmetric and therefore the bound is trivial (equal to zero) in
the odd case $N=2m+1$.
  Let $f$ be an arbitrary normalized symmetric operator monotone function and
let $<\cdot, \cdot >_{\rho,f}$ be the associated quantum Fisher information. In
this paper we conjecture the inequality $$ det (Cov_\rho(A_h,A_j)) \geq det
(\frac{f(0)}{2} < i[\rho, A_h],i[\rho,A_j] >_{\rho,f}) $$ that gives a
non-trivial bound for any natural number $N$ using the commutators $i[\rho,
A_h]$. The inequality has been proved in the cases $N=1,2$ by the joint efforts
of many authors. In this paper we prove the case N=3 for real matrices.


title:
Persistence of the 0.7 anomaly of quantum point contacts in high
  magnetic fields

abstract:
  The spin degeneracy of the lowest subband that carries one-dimensional
electron transport in quantum point contacts appears to be spontaneously lifted
in zero magnetic field due to a phenomenon that is known as the 0.7 anomaly. We
measured this energy splitting, and studied how it evolves into a splitting
that is the sum of the Zeeman effect and a field-independent exchange
contribution when applying a magnetic field. While this exchange contribution
shows sample-to-sample fluctuations, it is for all QPCs correlated with the
zero-field splitting of the 0.7 anomaly. This provides evidence that the
splitting of the 0.7 anomaly is dominated by this field-independent exchange
splitting.


title: Colloid-colloid and colloid-wall interactions in driven suspensions

abstract:
  We investigate the non-equilibrium fluid structure mediated forces between
two colloids driven through a suspension of mutually non-interacting Brownian
particles as well as between a colloid and a wall in stationary situations. We
solve the Smoluchowski equation in bispherical coordinates as well as with a
method of reflections, both in linear approximation for small velocities and
numerically for intermediate velocities, and we compare the results to a
superposition approximation considered previously. In particular we find an
enhancement of the friction (compared to the friction on an isolated particle)
for two colloids driven side by side as well as for a colloid traveling along a
wall. The friction on tailgating colloids is reduced. Colloids traveling side
by side experience a solute induced repulsion while tailgating colloids are
attracted to each other.


title: Non-perturbative embedding of local defects in crystalline materials

abstract:
  We present a new variational model for computing the electronic first-order
density matrix of a crystalline material in presence of a local defect. A
natural way to obtain variational discretizations of this model is to expand
the difference Q between the density matrix of the defective crystal and the
density matrix of the perfect crystal, in a basis of precomputed maximally
localized Wannier functions of the reference perfect crystal. This approach can
be used within any semi-empirical or Density Functional Theory framework.


title:
Solar-like oscillations in the metal-poor subgiant nu Indi: II. Acoustic
  spectrum and mode lifetime

abstract:
  Convection in stars excites resonant acoustic waves which depend on the sound
speed inside the star, which in turn depends on properties of the stellar
interior. Therefore, asteroseismology is an unrivaled method to probe the
internal structure of a star. We made a seismic study of the metal-poor
subgiant star nu Indi with the goal of constraining its interior structure. Our
study is based on a time series of 1201 radial velocity measurements spread
over 14 nights obtained from two sites, Siding Spring Observatory in Australia
and ESO La Silla Observatory in Chile. The power spectrum of the high precision
velocity time series clearly presents several identifiable peaks between 200
and 500 uHz showing regularity with a large and small spacing of 25.14 +- 0.09
uHz and 2.96 +- 0.22 uHz at 330 uHz. Thirteen individual modes have been
identified with amplitudes in the range 53 to 173 cm/s. The mode damping time
is estimated to be about 16 days (1-sigma range between 9 and 50 days),
substantially longer than in other stars like the Sun, the alpha Cen system or
the giant xi Hya.


title:
Continuous loading of $^{1}$S$_{0}$ calcium atoms into an optical dipole
  trap

abstract:
  We demonstrate an efficient scheme for continuous trap loading based upon
spatially selective optical pumping. We discuss the case of $^{1}$S$_{0}$
calcium atoms in an optical dipole trap (ODT), however, similar strategies
should be applicable to a wide range of atomic species. Our starting point is a
reservoir of moderately cold ($\approx 300 \mu$K) metastable
$^{3}$P$_{2}$-atoms prepared by means of a magneto-optic trap (triplet-MOT). A
focused 532 nm laser beam produces a strongly elongated optical potential for
$^{1}$S$_{0}$-atoms with up to 350 $\mu$K well depth. A weak focused laser beam
at 430 nm, carefully superimposed upon the ODT beam, selectively pumps the
$^{3}$P$_{2}$-atoms inside the capture volume to the singlet state, where they
are confined by the ODT. The triplet-MOT perpetually refills the capture volume
with $^{3}$P$_{2}$-atoms thus providing a continuous stream of cold atoms into
the ODT at a rate of $10^7 $s$^{-1}$. Limited by evaporation loss, in 200 ms we
typically load $5 \times 10^5$ atoms with an initial radial temperature of 85
$\mu$K. After terminating the loading we observe evaporation during 50 ms
leaving us with $10^5$ atoms at radial temperatures close to 40 $\mu$K and a
peak phase space density of $6.8 \times 10^{-5}$. We point out that a
comparable scheme could be employed to load a dipole trap with
$^{3}$P$_{0}$-atoms.


title: An Exceptional VHE Gamma-Ray Flare of PKS 2155-304

abstract:
  The high-frequency peaked BL Lac PKS 2155-304 at redshift z=0.116 is a
well-known VHE (>100 GeV) gamma-ray emitter. Since 2002 its VHE flux has been
monitored using the H.E.S.S. stereoscopic array of imaging
atmospheric-Cherenkov telescopes in Namibia. During the July 2006 dark period,
the average VHE flux was measured to be more than ten times typical values
observed from the object. This article focuses solely on an extreme gamma-ray
outburst detected in the early hours of July 28, 2006 (MJD 53944). The average
flux observed during this outburst is I(>200 GeV) = (1.72$\pm$$0.05_{\rm
stat}$$\pm$$0.34_{\rm syst}$) $\times$ 10$^{-9}$ cm$^{-2}$ s$^{-1}$,
corresponding to ~7 times the flux, I(>200 GeV), observed from the Crab Nebula.
Peak fluxes are measured with one-minute time scale resolution at more than
twice this average value. Variability is seen up to ~600 s in the Fourier power
spectrum, and well-resolved bursts varying on time scales of ~200 seconds are
observed. There are no strong indications for spectral variability within the
data. Assuming the emission region has a size comparable to the Schwarzschild
radius of a ~10$^9 M_\odot$ black hole, Doppler factors greater than 100 are
required to accommodate the observed variability time scales.


title: Stringy E-functions of hypersurfaces and of Brieskorn singularities

abstract:
  We show that for a hypersurface Batyrev's stringy E-function can be seen as a
residue of the Hodge zeta function, a specialization of the motivic zeta
function of Denef and Loeser. This is a nice application of inversion of
adjunction. If an affine hypersurface is given by a polynomial that is
non-degenerate with respect to its Newton polyhedron, then the motivic zeta
function and thus the stringy E-function can be computed from this Newton
polyhedron (by work of Artal, Cassou-Nogues, Luengo and Melle based on an
algorithm of Denef and Hoornaert). We use this procedure to obtain an easy way
to compute the contribution of a Brieskorn singularity to the stringy
E-function. As a corollary, we prove that stringy Hodge numbers of varieties
with a certain class of strictly canonical Brieskorn singularities are
nonnegative. We conclude by computing an interesting 6-dimensional example. It
shows that a result, implying nonnegativity of stringy Hodge numbers in lower
dimensional cases, obtained in our previous paper, is not true in higher
dimension.


title:
Symmetric Hamiltonian of the Garnier system and its degenerate systems
  in two variables

abstract:
  We present {\it symmetric Hamiltonians} for the degenerate Garnier systems in
two variables. For these symmetric Hamiltonians, we make the symmetry and
holomorphy conditions, and we also make a generalization of these systems
involving symmetry and holomorphy conditions inductively. We also show the
confluence process among each system by taking the coupling confluence process
of the Painlev\'e systems.

categories: math.AG math-ph math.AP math.CA math.DS math.MP


title:
A general track reconstruction scheme and its application to the OPERA
  drift tubes

abstract:
  A general reconstruction and calibration procedure for tracking and wire
position determination of the OPERA drift tubes is presented. The mathematics
of the pattern recognition and the track fit are explained.


title:
Upper Bounds on the Number of Vertices of Weight <=k in Particular
  Arrangements of Pseudocircles

abstract:
  In arrangements of pseudocircles (Jordan curves) the weight of a vertex
(intersection point) is the number of pseudocircles that contain the vertex in
its interior. We give improved upper bounds on the number of vertices of weight
<=k in certain arrangements of pseudocircles in the plane. In particular,
forbidding certain subarrangements we improve the known bound of 6n-12 (cf.
Kedem et al., 1986) for vertices of weight 0 in arrangements of n pseudocircles
to 4n-6. In complete arrangements (i.e. arrangements with each two
pseudocircles intersecting) we identify two subarrangements of three and four
pseudocircles, respectively, whose absence gives improved bounds for vertices
of weight 0 and more generally for vertices of weight <=k.


title: N2H+ and N2D+ in interstellar molecular clouds. II- Observations

abstract:
  We present observations of the $J$=1--0, 2--1, and 3--2 rotational
transitions of N$_2$H$^+$ and N$_2$D$^+$ towards a sample of prototypical dark
clouds. The data have been interpreted using non--local radiative transfer
models.


title: A search for solar-like oscillations in the Am star HD 209625

abstract:
  The goal is to test the structure of hot metallic stars, and in particular
the structure of a near-surface convection zone using asteroseismic
measurements. Indeed, stellar models including a detailed treatement of the
radiative diffusion predict the existence of a near-surface convection zone in
order to correctly reproduce the anomalies in surface abundances that are
observed in Am stars. The Am star HD 209625 was observed with the Harps
spectrograph mounted on the 3.6-m telescope at the ESO La Silla Observatory
(Chile) during 9 nights in August 2005. This observing run allowed us to
collect 1243 radial velocity (RV) measurements, with a standard deviation of
1.35 m/s. The power spectrum associated with these RV measurements does not
present any excess. Therefore, either the structure of the external layers of
this star does not allow excitation of solar-like oscillations, or the
amplitudes of the oscillations remain below 20-30 cm/s (depending on their
frequency range).


title:
Spherically symmeteric dark energy structure in the context of Chaplygin
  gas model

abstract:
  Spherically symmetric dark energy structures are investigated in the
framework of a generalized Chaplygin gas (GCG), which has an equation of state
of the form $P = - A/\rho^{\alpha}} $. We also study these in a modified GCG
equation of state, which includes a matter term, i.e. $P = \sigma^{2} \rho -
A/\rho^{\alpha}$. The results of the latter are then compared with some
observational data on low-surface-brightness galaxies which are supposed to be
dominated by dark matter.


title: Strong CP Violation in External Magnetic Fields

abstract:
  We study the response of the QCD vacuum to an external magnetic field, in the
presence of strong CP violation. Using chiral perturbation theory and large N_c
expansion, we show that the external field would polarize quantum fluctuations
and induce an electric dipole moment of the vacuum, along the direction of the
magnetic field. We estimate the magnitude of this effect in different physical
scenarios. In particular, we find that the polarization induced by the magnetic
field of a magnetar could accelerate electric charges up to energies of the
order \theta 10^3 TeV. We also suggest a connection with the possible existence
of "hot-spots" on the surface of neutron stars.


title: Notes on coherent backscattering from a random potential

abstract:
  We consider the quantum scattering from a random potential of strength
$\lambda^{1/2}$ and with a support on the scale of the mean free path, which is
of order $\lambda^{-1}$. On the basis of maximally crossed diagrams we provide
a concise formula for the backscattering rate in terms of the Green's function
for the kinetic Boltzmann equation. We briefly discuss the extension to wave
scattering.


title: Kinetic Equations for Quantum Many-Particle Systems

abstract:
  The current status of the derivation of kinetic equations from quantum
many-particle dynamics is reviewed.