title:
Variable accretion and emission from the stellar winds in the Galactic
  centre

abstract:
  We present numerical simulations of stellar wind dynamics in the central
parsec of the Galactic centre, studying in particular the accretion of gas on
to Sgr A*, the super-massive black hole. Unlike our previous work, here we use
state-of-the-art observational data on orbits and wind properties of individual
wind-producing stars. Since wind velocities were revised upwards and non-zero
eccentricities were considered, our new simulations show fewer clumps of cold
gas and no conspicuous disc-like structure. The accretion rate is dominated by
a few close `slow wind stars' v_w < 750 km/s, and is consistent with the Bondi
estimate, but variable on time-scales of tens to hundreds of years. This
variability is due to the stochastic in-fall of cold clumps of gas, as in
earlier simulations, and to the eccentric orbits of stars. The present models
fail to explain the high luminosity of Sgr A* a few hundred years ago implied
by Integral observations, but we argue that the accretion of a cold clump with
a small impact parameter could have caused it. Finally, we show the possibility
of constraining the total mass-loss rate of the `slow wind stars' using near
infra-red observations of gas in the central few arcseconds.


title: Elementary excitations in a supersolid

abstract:
  We study elementary low energy excitations inside a supersolid. We find that
the coupling between the longitudinal lattice vibration mode and the superfluid
mode leads to two longitudinal modes (one upper branch and one lower branch)
inside the supersolid, while the transverse modes in the supersolid stay the
same as those inside a normal solid. We also work out various experimental
signatures of these novel elementary excitations by evaluating the Debye-Waller
factor, density-density correlation, vortex loop-vertex loop interactions,
specific heat and excess entropy from the vacancies per mole.


title: Non-local effects on the heavy-ion fusion at sub-barrier energies

abstract:
  We investigate the effect of Pauli non-locality in the heavy-ion optical
potential on sub-barrier fusion reactions. The S\~{a}o Paulo potential, which
takes into account the Pauli non-locality and has been widely used in analyzing
elastic scattering, has also recently been applied to heavy-ion fusion.
However, the approximation employed in deriving the S\~{a}o Paulo potential,
based on the Perey-Buck semi-classical treatment of neutron induced reactions,
must be assessed for charged particles tunneling through a barrier. It is the
purpose of this note to look into this question. We consider the widely studied
system $^{16}$O + $^{208}$Pb at energies that span the barrier region from 10
MeV below to 10 MeV above. It seems that the non-locality plays a minor role.
We find the S\~{a}o Paulo potential to be quite adequate throughout the region.


title: Fourier-stable subrings in the Chow rings of abelian varieties

abstract:
  We study subrings in the Chow ring $\CH^*(A)_{{\Bbb Q}}$ of an abelian
variety $A$, stable under the Fourier transform with respect to an arbitrary
polarization. We prove that by taking Pontryagin products of classes of
dimension $\leq 1$ one gets such a subring. We also show how to construct
finite-dimensional Fourier-stable subrings in $\CH^*(A)_{{\Bbb Q}}$. Another
result concerns the relation between the Pontryagin product and the usual
product on the $\CH^*(A)_{{\Bbb Q}}$. We prove that the operator of the usual
product with a cycle is a differential operator with respect to the Pontryagin
product and compute its order in terms of the Beauville's decomposition of
$\CH^*(A)_{{\Bbb Q}}$.


title:
Revisiting the Fermi Golden Rule: Quantum Dynamical Phase Transition as
  a Paradigm Shift

abstract:
  Classical and quantum phase transitions involve observables which are
non-analytic as functions of a controlled thermodynamical variable. As occurs
with the self-consistent Fermi Golden Rule, one condition to obtain the
discontinuous behavior is the proper evaluation of a classical or quantum
thermodynamic limit. We show that in presence of an environment, the
oscillatory dynamics of a quantum two-level system, in analogy with a classical
damped oscillator, can undergo a quantum dynamical phase transition to a
non-oscillatory phase. This is obtained from a self-consistent solution of the
Generalized Landauer Buettiker Equations, a simplified integral form of the
Keldysh formalism. I argue that working at each side of the transition implies
standing under different paradigms in the Kuhn's sense of the word. In
consequence, paradigms incommensurability obtains a sound mathematical
justification as a consequence of the non-analyticity of the observables. A
strong case is made upon the need to deepen the public's intuition and
understanding on the abrupt transition from static to dynamical friction
regimes.
  Keywords: Self Consistent Fermi Golden Rule, Paradigm Shift, Quantum
Dynamical Phase Transition, Decoherence, Energy-time Wigner Function,
Dissipative Two-level system, Keldysh Formalisma, Generalized
Landauer-Buettiker Equations, Loschmidt Echo, Mesoscopic Echo, Spin Dynamics,
Solid State NMR, Dynamical Quantum Zeno Effect, Liquid Crystal NMR.


title: Stability of Polytropes

abstract:
  This paper is an investigation of the stability of some ideal stars. It is
in- tended as a study in General Relativity, with emphasis on the coupling to
matter, eventually aimed at a better understanding of very strong gravitational
fields and Black Holes. The work is based on an action principle for the
complete system of metric and matter fields. We propose a complete revision of
the treatment of boundary conditions. An ideal star in our terminology has
spherical symmetry and an isentropic equation of state. In our first work on
this subject it was assumed that the density vanishes beyond a finite distance
from the origin. But it is difficult to decide what the proper boundary
conditions should be and we are consequently skeptical of the concept of a
fixed boundary. In this paper we investigate the double polytrope,
characterized by a polytropic index n less than 5 in the bulk of the star and a
value larger than 5 in an outer atmosphere that extends to infinity. It has no
fixed boundary but a region of critical density where the polytropic index
changes from a value that is appropriate for the bulk of the star to a value
that provides a crude model for the atmosphere. The existence of a relation
between mass and radius is confirmed, as well as an upper limit on the mass.
The principal conclusion is that all the static configurations are stable.


title:
Clarifying Einstein's First Derivation for Mass-Energy Equivalence and
  Consequently Making Ives's Criticism a Void

abstract:
  We study physical situation considered by Einstein (Ann. Physik, 17, 1905)
for his first derivation of mass-energy equivalence. Einstein introduced a
constant $C$ in his derivation and reasoning surrounding $C$ and equations
containing $C$ caused criticism by Ives. Here we clarify Einstein's derivation
and obtain a value for constant $C$. The obtained zero value for $C$ suggests
alternative explanation for Einstein's derivation and makes Ives's criticism a
void and for which details are also presented in this paper.


title: Relatively computably enumerable reals

abstract:
  A real X is defined to be relatively c.e. if there is a real Y such that X is
c.e.(Y) and Y does not compute X. A real X is relatively simple and above if
there is a real Y <_T X such that X is c.e.(Y) and there is no infinite subset
Z of the complement of X such that Z is c.e.(Y). We prove that every nonempty
Pi^0_1 class contains a member which is not relatively c.e. and that every
1-generic real is relatively simple and above.


title: Binary Quantum Search

abstract:
  Database search has wide applications and is used as a subroutine in many
important algorithms. We shall consider a database with one target item.
Quantum algorithm finds the target item in a database faster than any classical
algorithm. It frequently occurs in practice that only a portion of information
about the target item is interesting, or we need to find a group of items
sharing some common feature as the target item. This problem is in general
formulated as search for a part of the database [a block] containing the target
item, instead of the item itself. This is partial search. Partial search trades
accuracy for speed, i.e. it works faster than a full search. Partial search
algorithm was discovered by Grover and Radhakrishnan. We shall consider
optimized version of the algorithm and call it GRK. It can be applied
successively [in a sequence]. First the database is partitioned into blocks and
we use GRK to find the target block. Then this target block is partitioned into
sub-blocks and we use GRK again to find the target sub-block. [We can call it
binary quantum search.] Another possibility is to partition the database into
sub-blocks directly and use GRK to find the target sub-block in one time. In
this paper we prove that the latter is faster [makes less queries to the
oracle].


title:
Simply connected minimal symplectic 4-manifolds with signature less than
  --1

abstract:
  For each pair $(e,\sigma)$ of integers satisfying $2e+3\sigma\ge 0$,
$\sigma\leq -2$, and $e+\sigma\equiv 0\pmod{4}$, with four exceptions, we
construct a minimal, simply connected symplectic 4-manifold with Euler
characteristic $e$ and signature $\sigma$. We also produce simply connected,
minimal symplectic 4-manifolds with signature zero (resp. signature -1) with
Euler characteristic $4k$ (resp. $4k+1$) for all $k\ge 46$ (resp. $k\ge 49$).


title: Ageing memory and glassiness of a driven vortex system

abstract:
  Many systems in nature, glasses, interfaces and fractures being some
examples, cannot equilibrate with their environment, which gives rise to novel
and surprising behaviour such as memory effects, ageing and nonlinear dynamics.
Unlike their equilibrated counterparts, the dynamics of out-of- equilibrium
systems is generally too complex to be captured by simple macroscopic laws.
Here we investigate a system that straddles the boundary between glass and
crystal: a Bragg glass formed by vortices in a superconductor. We find that the
response to an applied force evolves according to a stretched exponential, with
the exponent reflecting the deviation from equilibrium. After the force is
removed, the system ages with time and its subsequent response time scales
linearly with its age (simple ageing), meaning that older systems are slower
than younger ones. We show that simple ageing can occur naturally in the
presence of sufficient quenched disorder. Moreover, the hierarchical
distribution of timescales, arising when chunks of loose vortices cannot move
before trapped ones become dislodged, leads to a stretched-exponential
response.


title: Massive stars and globular cluster formation

abstract:
  We first present chemodynamical simulations to investigate how stellar winds
of massive stars influence early dynamical and chemical evolution of forming
globular clusters (GCs). In our numerical models, GCs form in
turbulent,high-density giant molecular clouds (GMCs), which are embedded in a
massive dark matter halo at high redshifts. We show how high-density, compact
stellar systems are formed from GMCs influenced both by physical processes
associated with star formation and by tidal fields of their host halos. We also
show that chemical pollution of GC-forming GMCs by stellar winds from massive
stars can result in star-to-star abundance inhomogeneities among light elements
(e.g., C, N, and O) of stars in GCs. The present model with a canonical initial
mass function (IMF) also shows a C-N anticorrelation that stars with smaller
[C/Fe] have larger [N/Fe] in a GC. Although these results imply that
``self-pollution'' of GC-forming GMCs by stellar winds from massive stars can
cause abundance inhomogeneities of GCs, the present models with different
parameters and canonical IMFs can not show N-rich stars with [N/Fe] ~ 0.8
observed in some GCs (e.g., NGC 6752). We discuss this apparent failure in the
context of massive star formation preceding low-mass one within GC-forming GMCs
(``bimodal star formation scenario''). We also show that although almost all
stars (~97%) show normal He abundances (Y) of ~0.24 some stars later formed in
GMCs can have Y as high as ~0.3 in some models. The number fraction of He-rich
stars with Y >0.26 is however found to be small (~10^-3) for most models.


title: Medical Image Segmentation and Localization using Deformable Templates

abstract:
  This paper presents deformable templates as a tool for segmentation and
localization of biological structures in medical images. Structures are
represented by a prototype template, combined with a parametric warp mapping
used to deform the original shape. The localization procedure is achieved using
a multi-stage, multi-resolution algorithm de-signed to reduce computational
complexity and time. The algorithm initially identifies regions in the image
most likely to contain the desired objects and then examines these regions at
progressively increasing resolutions. The final stage of the algorithm involves
warping the prototype template to match the localized objects. The algorithm is
presented along with the results of four example applications using MRI, x-ray
and ultrasound images.


title: Spectroscopy of moderately high-redshift RCS-1 clusters

abstract:
  We present spectroscopic observations of 11 moderately high-redshift (z~0.7-
1.0) clusters from the first Red-Sequence Cluster Survey (RCS-1). We find
excellent agreement between the red-sequence estimated redshift and the
spectroscopic redshift, with a scatter of 10% at z>0.7. At the high-redshift
end (z>~0.9) of the sample, we find two of the systems selected are projections
of pairs of comparably rich systems, with red-sequences too close to
discriminate in (R-z') colour. In one of these systems, the two components are
close enough to be physically associated. For a subsample of clusters with
sufficient spectroscopic members, we examine the correlation between B_gcR
(optical richness) and the dynamical mass inferred from the velocity
dispersion. We find these measurements to be compatible, within the relatively
large uncertainties, with the correlation established at lower redshift for the
X-ray selected CNOC1 clusters and also for a lower redshift sample of RCS-1
clusters. Confirmation of this and calibration of the scatter in the relation
will require larger samples of clusters at these and higher redshifts.
[abridged]


title:
Non-cooperative games for spreading code optimization, power control and
  receiver design in wireless data networks

abstract:
  This paper focuses on the issue of energy efficiency in wireless data
networks through a game theoretic approach. The case considered is that in
which each user is allowed to vary its transmit power, spreading code, and
uplink receiver in order to maximize its own utility, which is here defined as
the ratio of data throughput to transmit power. In particular, the case in
which linear multiuser detectors are employed at the receiver is treated first,
and, then, the more challenging case in which non-linear decision feedback
multiuser receivers are adopted is addressed. It is shown that, for both
receivers, the problem at hand of utility maximization can be regarded as a
non-cooperative game, and it is proved that a unique Nash equilibrium point
exists. Simulation results show that significant performance gains can be
obtained through both non-linear processing and spreading code optimization; in
particular, for systems with a number of users not larger than the processing
gain, remarkable gains come from spreading code optimization, while, for
overloaded systems, the largest gainscome from the use of non-linear
processing. In every case, however, the non-cooperative games proposed here are
shown to outperform competing alternatives.


title:
Using a Laguerre-Gaussian beam to trap and cool the rotational motion of
  a mirror

abstract:
  We show theoretically that it is possible to trap and cool the rotational
motion of a macroscopic mirror made of a perfectly reflecting spiral phase
element using orbital angular momentum transfer from a Laguerre-Gaussian
optical field. This technique offers a promising route to the placement of the
rotor in its quantum mechanical ground state in the presence of thermal noise.
It also opens up the possibility of simultaneously cooling a vibrational mode
of the same mirror. Lastly, the proposed design may serve as a sensitive
torsional balance in the quantum regime.


title:
Poloidal-toroidal decomposition in a finite cylinder. II.
  Discretization, regularization and validation

abstract:
  The Navier-Stokes equations in a finite cylinder are written in terms of
poloidal and toroidal potentials in order to impose incompressibility.
Regularity of the solutions is ensured in several ways: First, the potentials
are represented using a spectral basis which is analytic at the cylindrical
axis. Second, the non-physical discontinuous boundary conditions at the
cylindrical corners are smoothed using a polynomial approximation to a steep
exponential profile. Third, the nonlinear term is evaluated in such a way as to
eliminate singularities. The resulting pseudo-spectral code is tested using
exact polynomial solutions and the spectral convergence of the coefficients is
demonstrated. Our solutions are shown to agree with exact polynomial solutions
and with previous axisymmetric calculations of vortex breakdown and of
nonaxisymmetric calculations of onset of helical spirals. Parallelization by
azimuthal wavenumber is shown to be highly effective.


title: Peculiar Band Gap Structure of Graphene Nanoribbons

abstract:
  Graphene nanoribbons are quasi-one-dimensional meterials with finite width.
Characterizing a wide class of nanoribbons by edge shape and width, we make a
systematic analysis of their electronic properties. The band gap structure of
nanoribbons is shown to exhibit a valley structure with stream-like sequences
of metallic or almost metallic nanoribbons. Among them, all zigzag nanoribbons
are metallic, and armchair nanoribbons are metallic by period of 3. We find
that these stream-like sequences correspond to equi-width curves, and that the
band gap of chiral and armchair nanoribbons oscillate as a function of the
width. Furthermore a possible application of nanoribbons to nanoelectronics is
discussed.


title: On the gravitational coupling of Hadamard states

abstract:
  We study the constraints imposed by the Hadamard condition on the two-point
function of local states of a scalar quantum field conformally coupled to a
gravitational background. We propose a method to assign a stress tensor to the
state-dependent part of the two point function which arises as a conserved
tensor with an anomalous trace. To characterize the local Hadamard states of
physical interest we apply a super-selection rule relating this quantum stress
tensor to the matter stress tensor of a conformal invariant gravitational model
subject to a conformal symmetry breaking term. This implies that the
determination of a Hadamard state may be considered as an integral part of its
gravitational coupling via the back-reaction effect.


title: Nonlinear coupling of continuous variables at the single quantum level

abstract:
  We experimentally investigate nonlinear couplings between vibrational modes
of strings of cold ions stored in linear ion traps. The nonlinearity is caused
by the ions' Coulomb interaction and gives rise to a Kerr-type interaction
Hamiltonian H = n_r*n_s, where n_r,n_s are phonon number operators of two
interacting vibrational modes. We precisely measure the resulting oscillation
frequency shift and observe a collapse and revival of the contrast in a Ramsey
experiment. Implications for ion trap experiments aiming at high-fidelity
quantum gate operations are discussed.


title: On the construction of the Hadamard sates in two dimensions

abstract:
  The two dimensional analog of the Hadamard state condition is used to specify
the local Hadamard states associated with a linear quantum field coupled to a
two dimensional gravitational background. To characterize a local Hadamard
state corresponding to a physical vacuum state, we apply a superselection rule
in which the state dependent part of the two-point function is determined in
terms of a dynamical scalar field. It implies a basic connection between the
vacuum state and a scalar field coupled to gravity. We study the
characteristics of the Hadamard vacuum state through this superselection rule
using two different background metrics, the two dimensional analog of the
schwarzschild and FRW metric.


title:
Two-Dimensional Twisted Sigma Models, the Mirror Chiral de Rham Complex,
  and Twisted Generalised Mirror Symmetry

abstract:
  In this paper, we study the perturbative aspects of a "B-twisted"
two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle
$\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can
be naturally described in terms of the mathematical theory of ``Chiral
Differential Operators". In particular, the physical anomalies of the sigma
model can be reinterpreted as an obstruction to a global definition of the
associated sheaf of vertex superalgebras derived from the free conformal field
theory describing the model locally on $X$. In addition, one can also obtain a
novel understanding of the sigma model one-loop beta function solely in terms
of holomorphic data. At the $(2,2)$ locus, one can describe the resulting
half-twisted variant of the topological B-model in terms of a $\it{mirror}$
"Chiral de Rham complex" (or CDR) defined by Malikov et al. in \cite{GMS1}. Via
mirror symmetry, one can also derive various conjectural expressions relating
the sheaf cohomology of the mirror CDR to that of the original CDR on pairs of
Calabi-Yau mirror manifolds. An analysis of the half-twisted model on a
non-K\"ahler group manifold with torsion also allows one to draw conclusions
about the corresponding sheaves of CDR (and its mirror) that are consistent
with mathematically established results by Ben-Bassat in \cite{ben} on the
mirror symmetry of generalised complex manifolds. These conclusions therefore
suggest an interesting relevance of the sheaf of CDR in the recent study of
generalised mirror symmetry.


title: Towards a New Standard Model for Black Hole Accretion

abstract:
  We briefly review recent developments in black hole accretion disk theory,
emphasizing the vital role played by magnetohydrodynamic (MHD) stresses in
transporting angular momentum. The apparent universality of accretion-related
outflow phenomena is a strong indicator that large-scale MHD torques facilitate
vertical transport of angular momentum. This leads to an enhanced overall rate
of angular momentum transport and allows accretion of matter to proceed at an
interesting rate. Furthermore, we argue that when vertical transport is
important, the radial structure of the accretion disk is modified at small
radii and this affects the disk emission spectrum. We present a simple model
demonstrating how energetic, magnetically-driven outflows modify the emergent
disk emission spectrum with respect to that predicted by standard accretion
disk theory. A comparison of the predicted spectra against observations of
quasar spectral energy distributions suggests that mass accretion rates
inferred using the standard disk model may severely underestimate their true
values.


title: Larkin-Ovchinnikov-Fulde-Ferrell state in two-color quark matter

abstract:
  We explore the phase structure of two-color and two-flavor QCD in the space
of the quark chemical potential \mu_q and the isospin chemical potential \mu_I.
Using a mean-field model we calculate the chiral and diquark condensates,
\sigma and \Delta, self-consistently. In weak coupling and in the chiral limit,
we confirm the interval of the isospin chemical potential,
0.71\Delta_0<\mu_I<0.75\Delta_0, in which a single plane-wave
Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase is favored over isotropic
superfluidity and normal quark matter. The LOFF window becomes slightly wider
at high density. For stronger coupling with nonzero quark mass, which is
relevant to currently available numerical simulations in lattice two-color QCD,
the single plane-wave LOFF phase appears only at sufficiently high density. The
prediction obtained for the LOFF region could be tested with lattice since we
can prove that the present system is free from the fermion sign problem. We
draw the energy landscape on which local minima corresponding to the isotropic
superfluid phase and the LOFF phase and a local maximum corresponding to the
gapless phase are manifest. Our results clearly illustrate the path from the
the unstable gapless phase down to the LOFF phase.


title:
RossiXTE monitoring of 4U 1636-53: I. Long-term evolution and kHz
  Quasi-Periodic Oscillations

abstract:
  We have monitored the atoll-type neutron star low-mass X-ray binary 4U
1636-53 with the Rossi X-Ray Timing Explorer (RXTE) for more than 1.5 years.
Our campaign consisted of short (~2 ks) pointings separated by two days,
regularly monitoring the spectral and timing properties of the source. During
the campaign we observed a clear long-term oscillation with a period of ~30-40
days, already seen in the light curves from the RXTE All-Sky Monitor, which
corresponded to regular transitions between the hard (island) and soft (banana)
states. We detected kHz QPOs in about a third of the observations, most of
which were in the soft (banana) state. The distribution of the frequencies of
the peak identified as the lower kHz QPO is found to be different from that
previously observed in an independent data set. This suggests that the kHz QPOs
in the system shows no intrinsically preferred frequency.


title: Unparticle Physics in DIS

abstract:
  The unparticle stuff scenario related to the notrivial IR fixed point in
4D-conformal field theory is recently suggested by Georgi. We illustrate its
physical effects in Deep Inelastic Scattering (DIS) process. A possible signal
of unparticle related to parity violation asymmetry in DIS is investigated. It
is found out that the behavior of this parity violation signal is sensitive to
the value of the scale dimension $d_{\cal U}$ of unpaticle.


title: Distinguishability of Quantum States by Separable Operations

abstract:
  We study the distinguishability of multipartite quantum states by separable
operations. We first present a necessary and sufficient condition for a finite
set of orthogonal quantum states to be distinguishable by separable operations.
An analytical version of this condition is derived for the case of $(D-1)$ pure
states, where $D$ is the total dimension of the state space under
consideration. A number of interesting consequences of this result are then
carefully investigated. Remarkably, we show there exists a large class of
$2\otimes 2$ separable operations not being realizable by local operations and
classical communication. Before our work only a class of $3\otimes 3$ nonlocal
separable operations was known [Bennett et al, Phys. Rev. A \textbf{59}, 1070
(1999)]. We also show that any basis of the orthogonal complement of a
multipartite pure state is indistinguishable by separable operations if and
only if this state cannot be a superposition of 1 or 2 orthogonal product
states, i.e., has an orthogonal Schmidt number not less than 3, thus generalize
the recent work about indistinguishable bipartite subspaces [Watrous, Phys.
Rev. Lett. \textbf{95}, 080505 (2005)]. Notably, we obtain an explicit
construction of indistinguishable subspaces of dimension 7 (or 6) by
considering a composite quantum system consisting of two qutrits (resp. three
qubits), which is slightly better than the previously known indistinguishable
bipartite subspace with dimension 8.


title: Total Differential Errors in Two-Port Network Analyser Measurements

abstract:
  Since S-parameter measurements without uncertainty cannot claim any
credibility, the uncertainties in full two-port Vector Network Analyser (VNA)
measurements were estimated using total complex differentials (Total
Differential Errors). To express precisely a comparison relation between
complex differential errors, their differential error regions (DERs) were used.
To demonstrate the method in the most accurate case of a direct zero-length
thru, practical results are presented for commonly used Z-parameters of a
simple, two-port, DC resistive T-network, which was built and tested against
frequency with a VNA measurement system extended by two lengthy transmission
lines.


title:
Continuous time random walk, Mittag-Leffler waiting time and fractional
  diffusion: mathematical aspects

abstract:
  We show the asymptotic long-time equivalence of a generic power law waiting
time distribution to the Mittag-Leffler waiting time distribution,
characteristic for a time fractional CTRW. This asymptotic equivalence is
effected by a combination of "rescaling" time and "respeeding" the relevant
renewal process followed by a passage to a limit for which we need a suitable
relation between the parameters of rescaling and respeeding. Turning our
attention to spatially 1-D CTRWs with a generic power law jump distribution,
"rescaling" space can be interpreted as a second kind of "respeeding" which
then, again under a proper relation between the relevant parameters leads in
the limit to the space-time fractional diffusion equation. Finally, we treat
the `time fractional drift" process as a properly scaled limit of the counting
number of a Mittag-Leffler renewal process.

categories: cond-mat.stat-mech cond-mat.dis-nn math-ph math.MP


title: On the structure of positive maps between matrix algebras

abstract:
  A partial description of the structure of positive unital maps $\phi:
M_2(\bC) \to M_{n+1}(\bC)$ ($n\geq 2$) is given.


title:
Lattice dynamics of the Heisenberg chain coupled to finite frequency
  bond phonons

abstract:
  The phonon dynamics in a one dimensional Heisenberg spin chain coupled to
finite-frequency bond phonons is studied. We present the first detailed phonon
spectra for these systems using Quantum Monte Carlo. The quantum phase
transition is dominated by a central peak, yet the renormalisation of the main
phonon branch depends strongly on the bare phonon frequency omega_0. The main
branch remains largely unaffected at omega_0 \gsim J, but it softens completely
when omega_0 is low enough. This is an unusual scenario for a structural phase
transition and was observable only on sufficiently large systems. Approaching
the dimerized phase from finite temperature, the lattice dynamics mirrors the
behavior of a three dimensional system. For the efficient measurement of Greens
functions, we introduce a mapping from the stochastic series expansion to
continuous imaginary time.


title:
Non-uniform convergence of two-photon decay rates for excited atomic
  states

abstract:
  Two-photon decay rates in simple atoms such as hydrogenlike systems represent
rather interesting fundamental problems in atomic physics. The sum of the
energies of the two emitted photons has to fulfill an energy conservation
condition, the decay takes place via intermediate virtual states, and the total
decay rate is obtained after an integration over the energy of one of the
emitted photons. Here, we investigate cases with a virtual state having an
energy intermediate between the initial and the final state of the decay
process, and we show that due to non-uniform convergence, only a careful
treatment of the singularities infinitesimally displaced from the photon
integration contour leads to consistent and convergent results.


title: Two-Loop Effects and Current Status of the 4He+ Lamb Shift

abstract:
  We report on recent progress in the treatment of two-loop binding corrections
to the Lamb shift, with a special emphasis on S and P states. We use these and
other results in order to infer an updated theoretical value of the Lamb shift
in 4He+.


title: Two or Four: A Hint from Scalar Mesons in Radiative phi Decays ?

abstract:
  In this write-up, we summarize our recent analysis of radiative decays
involving light scalar mesons. Our analysis using the vector meson dominance
model at tree level indicates that it may be difficult to distinguish
$qq\bar{q}\bar{q}$ picture and $q\bar{q}$ picture for the light scalar nonet.
Our result on the process of $\phi \to \pi^0 \eta \gamma$ shows that the
derivative-type $f_0 K\bar{K}$ interaction reproduces experimental data below
950 GeV well, but gives a poor fit above 950 GeV, i.e., in the energy region
around the mass of $a_0(980)$, but that the discrepancy can be compensated by
the effect of the $K$ loop.


title: Re-visiting Direct $J/\psi$ Production at the Fermilab Tevatron

abstract:
  We re-analyze the direct $\jp$ production processes at the Fermilab Tevatron
in view of the recent observation at the B-factories, where both $\jp$
inclusive and exclusive production rates are found to be about an order of
magnitude larger than the leading order estimates of non-relativistic QCD. The
charm quark fragmentation to $\jp$, which is the dominant color-singlet process
at high $p_T$, is normalized by the B-factory measurements. The process
receives further enhancement due to the charm sea contribution which has so far
been ignored in most analyses. After summing up all sub-process contributions,
we find that the color-singlet mechanism alone can account for 20% to 90% of
the observed direct $\jp$ high $p_T$ production. The polarization rate of the
directly produced $\jp$ is sensitive to the fraction of the color-octet
contribution, which is employed to fill the gap between the color-singlet
prediction and experimental data. With a bigger $K$-factor for the charm quark
fragmentation probability, we envisage a smaller matrix element for the
color-octet $^3S_1^{(8)}$ state, and this can be examined at the LHC in near
future.


title:
The Fermi-Pasta-Ulam problem: periodic orbits, normal forms and
  resonance overlap criteria

abstract:
  Fermi, Pasta and Ulam observed, that the excitation of a low frequency normal
mode in a nonlinear acoustic chain leads to localization in normal mode space
on large time scales. Fast equipartition (and thus complete delocalization) in
the Fermi-Pasta-Ulam chain is restored if relevant intensive control parameters
exceed certain threshold values. We compare recent results on periodic orbits
(in the localization regime) and resonant normal forms (in a weak
delocalization regime), and relate them to various resonance overlap criteria.
We show that the approaches quantitatively agree in their estimate of the
localization-delocalization threshold. A key ingredient for this transition are
resonances of overtones.


title: Integrable Systems and Topology of Isospectral Manifolds

abstract:
  The well known Liouville-Arnold theorem says that if a level surface of
integrals of an integrable system is compact and connected, then it is a torus.
However, in some important examples of integrable systems the topology of a
level surface of integrals is quite complicated. This is due to the fact that
in these examples the phase space has points where either the Hamiltonian is
singular or the symplectic form is singular or degenerate. In such situations
the Liouville-Arnold theorem does not apply. However, sometimes it is possible
to define the corresponding flow on the whole level surface of integrals and
use this flow to investigate the topology. Tomei (1982) and Fried (1986) used
the Toda lattice to study the topology of the isospectral variety of Jacobi
matrices. We recall these results and we also expose new results concerning the
topology of the isospectral variety of zero-diagonal Jacobi matrices. This
topology is studied using the Volterra system.


title: Interval Conjectures for level Hilbert functions

abstract:
  We conjecture that the set of all Hilbert functions of (artinian) level
algebras enjoys a very natural form of regularity, which we call the {\em
Interval Conjecture} (IC): If, for some positive integer $\alpha $,
$(1,h_1,...,h_i,...,h_e)$ and $(1,h_1,...,h_i+\alpha ,...,h_e)$ are both level
$h$-vectors, then $(1,h_1,...,h_i+\beta ,...,h_e)$ is also level for each
integer $\beta =0,1,..., \alpha .$ In the Gorenstein case, i.e. when $h_e=1$,
we also supply the {\em Gorenstein Interval Conjecture} (GIC), which naturally
generalizes the IC, and basically states that the same property simultaneously
holds for any two symmetric entries, say $h_i$ and $h_{e-i}$, of a Gorenstein
$h$-vector.
  These conjectures are inspired by the research performed in this area over
the last few years. A series of recent results seems to indicate that it will
be nearly impossible to characterize explicitly the sets of all Gorenstein or
of all level Hilbert functions. Therefore, our conjectures would at least
provide the existence of a very strong - and natural - form of order in the
structure of such important and complicated sets.
  We are still far from proving the conjectures at this point. However, we will
already solve a few interesting cases, especially when it comes to the IC, in
this paper. Among them, that of Gorenstein $h$-vectors of socle degree 4, that
of level $h$-vectors of socle degree 2, and that of non-unimodal level
$h$-vectors of socle degree 3 and any given codimension.


title:
Electromagnetic field quantization in a magnetodielectric medium with
  external charges

abstract:
  The electromagnetic field inside a cubic cavity filled up with a linear
magnetodielectric medium and in the presence of external charges is quantized
by modelling the magnetodielectric medium with two independent quantum fields.
Electric and magnetic polarization densities of the medium are defined in terms
of the ladder operators of the medium and eigenmodes of the cavity. Maxwell and
constitutive equations of the medium together with the equation of motion of
the charged particles have been obtained from the Heisenberg equations using a
minimal coupling scheme. Spontaneous emission of a two level atom embedded in a
magnetodielectric medium is calculated in terms of electric and magnetic
susceptibilities of the medium and the Green function of the cubic cavity as an
application of the model.


title: Uniqueness and non-uniqueness of chains on half lines

abstract:
  We establish a one-to-one correspondence between one-sided and two-sided
regular systems of conditional probabilities on the half-line that preserves
the associated chains and Gibbs measures. As an application, we determine
uniqueness and non-uniqueness regimes in one-sided versions of ferromagnetic
Ising models with long range interactions. Our study shows that the interplay
between chain and Gibbsian theories yields more information than that contained
within the known theory of each separate framework. In particular: (i) A
Gibbsian construction due to Dyson yields a new family of chains with phase
transitions; (ii) these transitions show that a square summability uniqueness
condition of chains is false in the general non-shift-invariant setting, and
(iii) an uniqueness criterion for chains shows that a Gibbsian conjecture due
to Kac and Thompson is false in this half-line setting.


title: Dune formation on the present Mars

abstract:
  We apply a model for sand dunes to calculate formation of dunes on Mars under
the present Martian atmospheric conditions. We find that different dune shapes
as those imaged by Mars Global Surveyor could have been formed by the action of
sand-moving winds occuring on today's Mars. Our calculations show, however,
that Martian dunes could be only formed due to the higher efficiency of Martian
winds in carrying grains into saltation. The model equations are solved to
study saltation transport under different atmospheric conditions valid for
Mars. We obtain an estimate for the wind speed and migration velocity of
barchan dunes at different places on Mars. From comparison with the shape of
bimodal sand dunes, we find an estimate for the timescale of the changes in
Martian wind regimes.


title:
Constraints on CPT violation from WMAP three year polarization data: a
  wavelet analysis

abstract:
  We perform a wavelet analysis of the temperature and polarization maps of the
Cosmic Microwave Background (CMB) delivered by the WMAP experiment in search
for a parity violating signal. Such a signal could be seeded by new physics
beyond the standard model, for which the Lorentz and CPT symmetries may not
hold. Under these circumstances, the linear polarization direction of a CMB
photon may get rotated during its cosmological journey, a phenomenon also
called cosmological birefringence. Recently, Feng et al. have analyzed a subset
the WMAP and BOOMERanG 2003 angular power spectra of the CMB, deriving a
constraint that mildly favors a non zero rotation. By using wavelet transforms
we set a tighter limit on the CMB photon rotation angle \Delta\alpha= -2.5 \pm
3.0 (\Delta\alpha= -2.5 \pm 6.0) at the one (two) \sigma level, consistent with
a null detection.


title:
Set of equations for transient enhanced diffusion in shallow
  ion-implanted layers

abstract:
  To simulate the transient enhanced diffusion near the surface or interface, a
set of equations describing the impurity diffusion and quasichemical reactions
of dopant atoms and point defects in ion-implanted layers is proposed and
analyzed. The diffusion equations obtained take into account different charge
states of mobile or immobile species and drift the mobile species in the
built-in electric field and field of elastic stresses. The absorption of
self-interstitials on the surface and drift of the defects due to elastic
stresses result in the nonuniform distributions of point defects. It was shown
analytically and by means of numerical calculations that consideration of the
nonuniform defect distributions enables one to explain the phenomenon of
"uphill" impurity diffusion near the surface during annealing of ion-implanted
layers. The performed calculations of the boron concentration profile after
annealing of a shallow implanted layer agree well with the experimental data
confirming the efficiency of the proposed equations.


title:
Search for third-generation leptoquarks in ppbar collisions at
  sqrt(s)=1.96 TeV

abstract:
  We report on a search for charge-1/3 third-generation leptoquarks (LQ)
produced in ppbar collisions at sqrt(s)=1.96 TeV using the D0 detector at
Fermilab. Third generation leptoquarks are assumed to be produced in pairs and
to decay to a tau neutrino and a b quark with branching fraction B. We place
upper limits on sigma(ppbar->LQLQbar)*B^2 as a function of the leptoquark mass
M_{LQ}. Assuming B=1, we exclude at the 95% confidence level third-generation
scalar leptoquarks with M_{LQ} < 229 GeV.


title:
Conductance of a junction between a normal metal and a Berezinskii
  superconductor

abstract:
  The conductance of a junction between a normal metal and a superconductor
having the symmetry proposed by Berezinskii is studied theoretically. The main
feature of this symmetry is the odd frequency dependence of the anomalous Green
function, which makes possible the s-wave triplet superconducting state (the
Berezinskii superconductor). The Andreev reflection (which links positive and
negative energies) is sensitive to the energetic symmetry; as a result, the
conductance of the junction involving the Berezinskii superconductor is
qualitatively different from the case of a conventional superconductor.
Experimentally, the obtained results can be employed to test the possibility of
the Berezinskii superconductivity proposed for Na$_x$CoO$_2$ and to identify
the odd-omega component predicted for superconductor-ferromagnet junctions.


title:
Real singular Del Pezzo surfaces and threefolds fibred by rational
  curves, I

abstract:
  Let W -> X be a real smooth projective threefold fibred by rational curves.
Koll\'ar proved that if W(R) is orientable a connected component N of W(R) is
essentially either a Seifert fibred manifold or a connected sum of lens spaces.
Let k : = k(N) be the integer defined as follows: If g : N -> F is a Seifert
fibration, one defines k : = k(N) as the number of multiple fibres of g, while,
if N is a connected sum of lens spaces, k is defined as the number of lens
spaces different from P^3(R). Our Main Theorem says: If X is a geometrically
rational surface, then k <= 4. Moreover we show that if F is diffeomorphic to
S^1xS^1, then W(R) is connected and k = 0. These results answer in the
affirmative two questions of Koll\'ar who proved in 1999 that k <= 6 and
suggested that 4 would be the sharp bound. We derive the Theorem from a careful
study of real singular Del Pezzo surfaces with only Du Val singularities.


title: Overview of the Netsukuku network

abstract:
  Netsukuku is a P2P network system designed to handle a large number of nodes
with minimal CPU and memory resources. It can be easily used to build a
worldwide distributed, anonymous and not controlled network, separated from the
Internet, without the support of any servers, ISPs or authority controls. In
this document, we give a generic and non technical description of the Netsukuku
network, emphasizing its main ideas and features.


title:
$\pi^0$ photoproduction on the proton for photon energies from 0.675 to
  2.875 GeV

abstract:
  Differential cross sections for the reaction $\gamma p \to p \pi^0$ have been
measured with the CEBAF Large Acceptance Spectrometer (CLAS) and a tagged
photon beam with energies from 0.675 to 2.875 GeV. The results reported here
possess greater accuracy in the absolute normalization than previous
measurements. They disagree with recent CB-ELSA measurements for the process at
forward scattering angles. Agreement with the SAID and MAID fits is found below
1 GeV. The present set of cross sections has been incorporated into the SAID
database, and exploratory fits have been extended to 3 GeV. Resonance couplings
have been extracted and compared to previous determinations.


title: Quantum Shortest Path Netsukuku

abstract:
  This document describes the QSPN, the routing discovery algorithm used by
Netsukuku. Through a deductive analysis the main proprieties of the QSPN are
shown. Moreover, a second version of the algorithm, is presented.


title:
k-dependent SU(4) model of high-temperature superconductivity and its
  coherent-state solutions

abstract:
  We extend the SU(4) model [1-5] for high-Tc superconductivity to an SU(4)k
model that permits explicit momentum (k) dependence in predicted observables.
We derive and solve gap equations that depend on k, temperature, and doping
from the SU(4)k coherent states, and show that the new SU(4)k model reduces to
the original SU(4) model for observables that do not depend explicitly on
momentum. The results of the SU(4)k model are relevant for experiments such as
ARPES that detect explicitly k-dependent properties. The present SU(4)k model
describes quantitatively the pseudogap temperature scale and may explain why
the ARPES-measured T* along the anti-nodal direction is larger than other
measurements that do not resolve momentum. It also provides an immediate
microscopic explanation for Fermi arcs observed in the pseudogap region. In
addition, the model leads to a prediction that even in the underdoped regime,
there exist doping-dependent windows around nodal points in the k-space, where
antiferromagnetism may be completely suppressed for all doping fractions,
permitting pure superconducting states to exist.


title: The Netsukuku network topology

abstract:
  In this document, we describe the fractal structure of the Netsukuku
topology. Moreover, we show how it is possible to use the QSPN v2 on the high
levels of the fractal.


title: ANDNA: the distributed hostname management system of Netsukuku

abstract:
  We present the Abnormal Netsukuku Domain Name Anarchy system. ANDNA is the
distributed, non hierarchical and decentralised system of hostname management
used in the Netsukuku network.


title: Restricted infinitesimal deformations of restricted simple Lie algebras

abstract:
  We compute the restricted infinitesimal deformations of the restricted simple
Lie algebras over an algebraically closed field of characteristic different
from 2 and 3.


title:
The Origin of Fermi Arcs in Cuprate Pseudogap States and Strong
  Constraints on Viable Theories of High-Temperature Superconductivity

abstract:
  A full Fermi surface exists in underdoped high-temperature superconductors if
the temperature T lies above the pseudogap temperature T*. Below T* only arcs
of Fermi surface survive, scaling with T/T* as T -> 0, with T* displaying
strong doping dependence. There is no accepted explanation for this behavior.
We show that generalizing the BCS theory of normal superconductivity to include
d-wave pairs and antiferromagnetism leads to the origin and doping dependence
of the T* scale, and a quantitative description of Fermi arcs. These results
place strong constraints on viable theories of high-temperature
superconductivity.


title:
Plastic response of a 2D amorphous solid to quasi-static shear : I -
  Transverse particle diffusion and phenomenology of dissipative events

abstract:
  We perform extensive simulations of a 2D LJ glass subjected to quasi-static
shear deformation at T=0. We analyze the distribution of non-affine
displacements in terms of contributions of plastic, irreversible events, and
elastic, reversible motions. From this, we extract information about
correlations between plastic events and about the elastic non-affine noise.
Moreover, we find that non-affine motion is essentially diffusive, with a
clearly size-dependent diffusion constant. These results, supplemented by close
inspection of the evolving patterns of the non-affine tangent displacement
field, lead us to propose a phenomenology of plasticity in such amorphous
media. It can be schematized in terms of elastic loading and irreversible flips
of small, randomly located shear transformation zones, elastically coupled via
their quadrupolar fields.


title:
A Microscpoic Model for the Neutron Dynamic Structure Factor of Solid
  Methane in phase II

abstract:
  We have constructed an approximate microscopic model for the neutron dynamic
structure factor of solid methane in phase II. We expect our model to apply for
neutron energies below 1\textit{eV} at pressures near 1 bar and temperatures
below 20K, where solid methane exists in a phase, called phase II, in which the
tetrahedral hydrogens exist in a mixed phase of free rotors and hindered
rotors. Certain matrix elements needed for the dynamic structure factor $S(Q,
\omega)$ are adapted from a calculation by Ozaki \textit{et
al.}\cite{ozaki:3442}\cite{ozaki2}. The model treats the effects of molecular
translations, intramolecular vibrations and the free and hindered rotational
degrees of freedom as uncoupled ones. Total scattering cross sections
calculated from the model agree with the cross section measurements of
Grieger\cite{grieger:3161} and Whittemore\cite{Wittemore} for the incident
neutron energies of 0.5 \textit{meV} $\sim$ 1\textit{eV}. The effective density
of states extracted from the model was compared with the Harker $&$ Brugger
frequency spectrum extracted from neutron scattering measurements conducted at
22K\cite{HARKER1967}.


title: Einstein's Theory of Gravity in the Presence of Pressure: A Review

abstract:
  The mysterious `dark energy' needed to explain the current observations,
poses a serious confrontation between fundamental physics and cosmology. The
present crisis may be an outcome of the (so far untested) prediction of the
general theory of relativity that the pressure of the matter source also
gravitates. In this view, a theoretical analysis reveals some surprising
inconsistencies and paradoxes faced by the energy-stress tensor (in the
presence of pressure) which is used to model the matter content of the
universe, including dark energy.


abstract:
  Integrated light in direct excitation and energy transfer luminescence has
been investigated. In the investigations reported here, monomolecular centers
were taken into account. It was found that the integrated light is equal to the
product of generation rate and time of duration of excitation pulse for both
direct excitation and energy transfer luminescence.


title:
A Metric for Gradient RG Flow of the Worldsheet Sigma Model Beyond First
  Order

abstract:
  Tseytlin has recently proposed that an action functional exists whose
gradient generates to all orders in perturbation theory the Renormalization
Group (RG) flow of the target space metric in the worldsheet sigma model. The
gradient is defined with respect to a metric on the space of coupling constants
which is explicitly known only to leading order in perturbation theory, but at
that order is positive semi-definite, as follows from Perelman's work on the
Ricci flow. This gives rise to a monotonicity formula for the flow which is
expected to fail only if the beta function perturbation series fails to
converge, which can happen if curvatures or their derivatives grow large. We
test the validity of the monotonicity formula at next-to-leading order in
perturbation theory by explicitly computing the second-order terms in the
metric on the space of coupling constants. At this order, this metric is found
not to be positive semi-definite. In situations where this might spoil
monotonicity, derivatives of curvature become large enough for higher order
perturbative corrections to be significant.


title:
Enhancement of Noisy Planar Nuclear Medicine Images using Mean Field
  Annealing

abstract:
  Nuclear medicine (NM) images inherently suffer from large amounts of noise
and blur. The purpose of this research is to reduce the noise and blur while
maintaining image integrity for improved diagnosis. The proposed solution is to
increase image quality after the standard pre- and post-processing undertaken
by a gamma camera system. Mean Field Annealing (MFA) is the image processing
technique used in this research. It is a computational iterative technique that
makes use of the Point Spread Function (PSF) and the noise associated with the
NM image. MFA is applied to NM images with the objective of reducing noise
while not compromising edge integrity. Using a sharpening filter as a
post-processing technique (after MFA) yields image enhancement of planar NM
images.


title: Conductance Spectroscopy of Spin-triplet Superconductors

abstract:
  We propose a novel experiment to identify the symmetry of superconductivity
on the basis of theoretical results for differential conductance of a normal
metal connected to a superconductor. The proximity effect from the
superconductor modifies the conductance of the remote current depending
remarkably on the pairing symmetry: spin-singlet or spin-triplet. The clear-cut
difference in the conductance is explained by symmetry of Cooper pairs in a
normal metal with respect to frequency. In the spin-triplet case, the anomalous
transport is realized due to an odd-frequency symmetry of Cooper pairs.


title:
On the refractive index for a nonmagnetic two-component medium:
  resolution of a controversy

abstract:
  The refractive index of a dielectric medium comprising both passive and
inverted components in its permittivity was determined using two methods: (i)
in the time domain, a finite-difference algorithm to compute the
frequency-domain reflectance from reflection data for a pulsed plane wave that
is normally incident on a dielectric half-space, and (ii) in the frequency
domain, the deflection of an obliquely incident Gaussian beam on transmission
through a dielectric slab. The dielectric medium was found to be an active
medium with a negative real part for its refractive index. Thereby, a recent
controversy in the scientific literature was resolved.


title:
Exploring cloudy gas accretion as a source of interstellar turbulence in
  the outskirts of disks

abstract:
  High--resolution 2D--MHD numerical simulations have been carried out to
investigate the effects of continuing infall of clumpy gas in extended HI
galactic disks. Given a certain accretion rate, the response of the disk
depends on its surface gas density and temperature. For Galactic conditions at
a galactocentric distance of ~20 kpc, and for mass accretion rates consistent
with current empirical and theoretical determinations in the Milky Way, the
rain of compact high velocity clouds onto the disk can maintain transonic
turbulent motions in the warm phase (~2500 K) of HI. Hence, the HI line width
is expected to be ~6.5 km/s for a gas layer at 2500 K, if infall were the only
mechanism of driving turbulence. Some statistical properties of the resulting
forcing flow are shown in this Letter. The radial dependence of the gas
velocity dispersion is also discussed.


title:
A Berry-Esseen type inequality for convex bodies with an unconditional
  basis

abstract:
  We provide a sharp rate of convergence in the central limit theorem for
random vectors with an unconditional, log-concave density. The argument relies
on analysis of the Neumann laplacian on convex domains and on the theory of
optimal transportation of measures.


title:
High-Resolution Scanning Tunneling Microscopy Imaging of Mesoscopic
  Graphene Sheets on an Insulating Surface

abstract:
  We present scanning tunneling microscopy (STM) images of single-layer
graphene crystals examined under ultrahigh vacuum conditions. The samples, with
lateral dimensions on the micron scale, were prepared on a silicon dioxide
surface by direct exfoliation of single crystal graphite. The single-layer
films were identified using Raman spectroscopy. Topographic images of
single-layer samples display the honeycomb structure expected for the full
hexagonal symmetry of an isolated graphene monolayer. The absence of observable
defects in the STM images is indicative of the high quality of these films.
Crystals comprised of a few layers of graphene were also examined. They
exhibited dramatically different STM topography, displaying the reduced
three-fold symmetry characteristic of the surface of bulk graphite.


title: Universal deformation rings and dihedral 2-groups

abstract:
  Let $k$ be an algebraically closed field of characteristic 2, and let $W$ be
the ring of infinite Witt vectors over $k$. Suppose $D$ is a dihedral 2-group.
We prove that the universal deformation ring $R(D,V)$ of an endo-trivial
$kD$-module $V$ is always isomorphic to $W[\mathbb{Z}/2\times\mathbb{Z}/2]$. As
a consequence we obtain a similar result for modules $V$ with stable
endomorphism ring $k$ belonging to an arbitrary nilpotent block with defect
group $D$. This confirms for such $V$ conjectures on the ring structure of the
universal deformation ring of $V$ which had previously been shown for $V$
belonging to cyclic blocks or to blocks with Klein four defect groups.


title:
Vibrational Infrared Lifetime of the Anesthetic nitrous oxide gas in
  solution

abstract:
  The lifetime of the asymmetric fundamental stretching 2218 cm$^{-1}$
vibration of the anesthetic gas nitrous oxide (N$_2$O) dissolved in octanol and
olive oil is reported. These solvents are model systems commonly used to assess
anesthetic potency. Picosecond time-scale molecular dynamics simulations have
suggested that protein dynamics or membrane dynamics play a role in the
molecular mechanism of anesthetic action. Ultrafast infrared spectroscopy with
100 fs time resolution is an ideal tool to probe dynamics of anesthetic
molecules on such timescales. Pump-probe studies at the peak of the vibrational
band yield a lifetime of $55 \pm 1$ ps in olive oil and $52 \pm 1 ps$ in
octanol. The similarity of lifetimes suggests that energy relaxation of the
anesthetic is determined primarily by the hydrophobic nature of the
environment, consistent with models of anesthetic action. The results show that
nitrous oxide is a good model system for probing anesthetic-solvent
interactions using nonlinear infrared spectroscopy.


title:
Analyticity of layer potentials and $L^{2}$ solvability of boundary
  value problems for divergence form elliptic equations with complex
  $L^{\infty}$ coefficients

abstract:
  We consider divergence form elliptic operators of the form $L=-\dv
A(x)\nabla$, defined in $R^{n+1} = \{(x,t)\in R^n \times R \}$, $n \geq 2$,
where the $L^{\infty}$ coefficient matrix $A$ is $(n+1)\times(n+1)$, uniformly
elliptic, complex and $t$-independent. We show that for such operators,
boundedness and invertibility of the corresponding layer potential operators on
$L^2(\mathbb{R}^{n})=L^2(\partial\mathbb{R}_{+}^{n+1})$, is stable under
complex, $L^{\infty}$ perturbations of the coefficient matrix. Using a variant
of the $Tb$ Theorem, we also prove that the layer potentials are bounded and
invertible on $L^2(\mathbb{R}^n)$ whenever $A(x)$ is real and symmetric (and
thus, by our stability result, also when $A$ is complex, $\Vert
A-A^0\Vert_{\infty}$ is small enough and $A^0$ is real, symmetric, $L^{\infty}$
and elliptic). In particular, we establish solvability of the Dirichlet and
Neumann (and Regularity) problems, with $L^2$ (resp. $\dot{L}^2_1)$ data, for
small complex perturbations of a real symmetric matrix. Previously, $L^2$
solvability results for complex (or even real but non-symmetric) coefficients
were known to hold only for perturbations of constant matrices (and then only
for the Dirichlet problem), or in the special case that the coefficients
$A_{j,n+1}=0=A_{n+1,j}$, $1\leq j\leq n$, which corresponds to the Kato square
root problem.


title:
Bounds on Unparticles Couplings to Electrons: from Electron g-2 to
  Positronium Decays

abstract:
  Unparticles as suggested recently by Georgi have surprising phenomenological
implications, distinctive from any other new physics that we know of. But they
must interact very feebly with ordinary matter to have avoided detection thus
far. We determine how feebly they can interact with the electron, using the
precisely measured quantities in QED: the electron g-2 and the bounds on
invisible and exotic positronium decays. The most stringent bound comes from
invisible ortho-positronium decays: the effective energy scale entering the
vector unparticle-electron interaction must exceed 4 x 10^5 TeV for a scaling
dimension 3/2 of the vector unparticle. The lower bounds on scales for other
unparticles range from a few tens to a few hundreds TeV. This makes the
detection of unparticles challenging in low energy electron systems.


title:
A Bell-Evans-Polanyi principle for molecular dynamics trajectories and
  its implications for global optimization

abstract:
  The Bell-Evans-Polanyi principle that is valid for a chemical reaction that
proceeds along the reaction coordinate over the transition state is extended to
molecular dynamics trajectories that in general do not cross the dividing
surface between the initial and the final local minima at the exact transition
state. Our molecular dynamics Bell-Evans-Polanyi principle states that low
energy molecular dynamics trajectories are more likely to lead into the basin
of attraction of a low energy local minimum than high energy trajectories. In
the context of global optimization schemes based on molecular dynamics our
molecular dynamics Bell-Evans-Polanyi principle implies that using low energy
trajectories one needs to visit a smaller number of distinguishable local
minima before finding the global minimum than when using high energy
trajectories.


title:
Dahlberg's bilinear estimate for solutions of divergence form complex
  elliptic equations

abstract:
  We consider divergence form elliptic operators $L=-\dv A(x)\nabla$, defined
in $\mathbb{R}^{n+1}=\{(x,t)\in\mathbb{R}^{n}\times\mathbb{R}\}, n \geq 2$,
where the $L^{\infty}$ coefficient matrix $A$ is $(n+1)\times(n+1)$, uniformly
elliptic, complex and $t$-independent. Using recently obtained results
concerning the boundedness and invertibility of layer potentials associated to
such operators, we show that if $Lu=0$ in $\mathbb{R}^{n+1}_+$, then for any
vector-valued ${\bf v} \in W^{1,2}_{loc},$ we have the bilinear estimate
$$|\iint_{\mathbb{R}^{n+1}_+} \nabla u \cdot \bar{{\bf v}} dx dt |\leq
C\sup_{t>0} \|u(\cdot,t)\|_{L^2(\mathbb{R}^n)}(\||t \nabla {\bf v}\|| +
\|N_*{\bf v}\|_{L^2(\mathbb{R}^n)}),$$ where $\||F\|| \equiv
(\iint_{\mathbb{R}^{n+1}_+} |F(x,t)|^2 t^{-1} dx dt)^{1/2},$ and where $N_*$ is
the usual non-tangential maximal operator. The result is new even in the case
of real symmetric coefficients, and generalizes the analogous result of
Dahlberg for harmonic functions on Lipschitz graph domains.


title:
A proof of the local $Tb$ Theorem for standard Calder\'{o}n-Zygmund
  operators

abstract:
  We give a proof of a so-called "local $Tb$" Theorem for singular integrals
whose kernels satisfy the standard Calder\'on-Zygmund conditions. The present
theorem, which extends an earlier result of M. Christ \cite{Ch}, was proved in
\cite{AHMTT} for "perfect dyadic" Calder\'on-Zygmund operators. The proof in
\cite{AHMTT} essentially carries over to the case considered here, with some
technical adjustments.


title:
Characteristics of Switchable Superconducting Flux Transformer with DC
  Superconducting Quantum Interference Device

abstract:
  We have investigated the flux transfer characteristics of a switchable flux
transformer comprising a superconducting loop and a DC superconducting quantum
interference device (DC-SQUID). This system can be used to couple multiple flux
qubits with a controllable coupling strength. Its characteristics were measured
using a flux input coil and a DC-SQUID for readout coupled to the transformer
loop in a dilution refrigerator. The observed characteristics are consistent
with the calculation results. We have demonstrated the reversal of the slope of
the characteristics and the complete switching off of the transformer, which
are useful features for its application as a controllable coupler for flux
qubits.


title:
PHENIX Measurement of High-$p_T$ Hadron-hadron and Photon-hadron
  Azimuthal Correlations

abstract:
  High-$p_T$ hadron-hadron correlations have been measured with the PHENIX
experiment in $\Cu$ and $\pp$ collisions at $\sqrt{s_{NN}}=200$ GeV. A
comparison of the jet widths and yields between the two colliding systems
allows us to study the medium effect on jets. We also present a first
measurement of direct photon-hadron correlations in $\Au$ and $\pp$ collisions.
We find that the near-side yields are consistent with zero in both systems. By
comparing the jet yields on the away side, we observe a suggestion of the
expected suppression of hadrons associated with photons in $\Au$ collisions.


title: Simulation via Direct Computation of Partition Functions

abstract:
  In this paper, we demonstrate the efficiency of simulations via direct
computation of the partition function under various macroscopic conditions,
such as different temperatures or volumes. The method can compute partition
functions by flattening histograms, through the Wang-Landau recursive scheme,
outside the energy space. This method offers a more general and flexible
framework for handling various types of ensembles, especially the ones in which
computation of the density of states is not convenient. It can be easily scaled
to large systems, and it is flexible in incorporating Monte Carlo cluster
algorithms or molecular dynamics. High efficiency is shown in simulating large
Ising models, in finding ground states of simple protein models, and in
studying the liquid-vapor phase transition of a simple fluid. The method is
very simple to implement and we expect it to be efficient in studying complex
systems with rugged energy landscapes, e.g., biological macromolecules.


title: Algebraic K-theory of hyperbolic 3-simplex reflection groups

abstract:
  A hyperbolic 3-simplex reflection group is a Coxeter group arising as a
lattice in the isometry group of hyperbolic 3-space, with fundamental domain a
geodesic simplex (possibly with some ideal vertices). The classification of
these groups is known, and there are exactly 9 cocompact examples, and 23
non-cocompact examples. We provide a complete computation of the lower
algebraic K-theory of the integral group ring of all the hyperbolic 3-simplex
reflection groups.


title:
The Quantum World is an AdS_5 with the Quantum Relativity Symmetry
  SO(2,4)

abstract:
  Quantum relativity as a generalized, or rather deformed, version of Einstein
relativity with a linear realization on a classical six-geometry beyond the
familiar setting of space-time offer a new framework to think about the quantum
space-time structure. The formulation requires two deformations to be
implemented through imposing two fundamental invariants. We take them to be the
independent Planck mass and Planck length. Together, they gives the quantum
$\hbar$. The scheme leads to {\small \boldmath\protect SO(2,4)} as the
relativity symmetry. The quantum world has an AdS$_5$ `classical' geometry,
which is parallel to the "conformal universe", but not scale invariant.


title: Resonating singlet valence plaquettes

abstract:
  We consider the simplest generalizations of the valence bond physics of SU(2)
singlets to SU(N) singlets that comprise objects with N sites -- these are
SU(N) singlet plaquettes with N=3 and N=4 in three spatial dimensions.
Specifically, we search for a quantum mechanical liquid of such objects -- a
resonating singlet valence plaquette phase that generalizes the celebrated
resonating valence bond phase for SU(2) spins. We extend the Rokhsar-Kivelson
construction of the quantum dimer model to the simplest SU(4) model for valence
plaquette dynamics on a cubic lattice. The phase diagram of the resulting
quantum plaquette model is analyzed both analytically and numerically. We find
that the ground state is solid everywhere, including at the Rokhsar-Kivelson
point where the ground state is an equal amplitude sum. By contrast, the equal
amplitude sum of SU(3) singlet triangular plaquettes on the face centered cubic
lattice is liquid and thus a candidate for describing a resonating single
valence plaquette phase, given a suitably defined local Hamiltonian.


title:
Optical properties of Er3+ doped alkali-chloro phosphate glasses for
  optical amplifiers

abstract:
  A new class of Erbium doped glasses with compositions xNa2O - (60-x)PbCl2 -
40P2O5 (x=0, 10, 20 and 30) were fabricated and characterized for optical
properties. Absorption spectra were analyzed for important Judd-Ofelt
parameters from the integrated intensities of various Er3+ glass absorption
bands. Photoluminescence (PL) and its decay behavior studies were carried out
for the transition 4I13/2 -> 4I15/2. A systematic correlation between the
Judd-Ofelt parameter {omega}2 and the covalent nature of the glass matrix was
observed, due to increased role of bridging oxygens in the glass network. The
PL broadness and life times of 4I13/2_> 4I15/2 transition were typically in the
range of 40-60nm and 2.13-2.5ms respectively. These glasses broadly showed high
transparency, high refractive index, shorter life times and, most importantly,
these glasses were found to be capable of being doped with larger
concentrations of Er3+ (up to 4 wt%). Increase of Er3+ concentration resulted
in the increase in PL line-widths with no significant effect of concentration
quenching, indicating that these glasses are suitable for optical
fibre/waveguide amplifiers.


title:
Preferential Detachment in Broadcast Signaling Networks: Connectivity
  and Cost Trade-off

abstract:
  We consider a network of nodes distributed in physical space without physical
links communicating through message broadcasting over specified distances.
Typically, communication using smaller distances is desirable due to savings in
energy or other resources. We introduce a network formation mechanism to enable
reducing the distances while retaining connectivity. Nodes, which initially
transmit signals at a prespecified maximum distance, subject links to
preferential detachment by autonomously decreasing their transmission radii
while satisfying conditions of zero communication loss and fixed maximum
node-hopping distance for signaling. Applied to networks with various spatial
topologies, we find cost reductions as high as 90% over networks that are
restricted to have all nodes with equal transmission distance.


title:
Enhanced sensitivity to variation of the fine structure constant and
  m_p/m_e in diatomic molecules

abstract:
  Sensitivity to temporal variation of the fundamental constants may be
strongly enhanced in transitions between narrow close levels of different
nature. This enhancement may be realized in a large number of molecules due to
cancelation between the ground state fine structure omega_f and vibrational
interval omega_v (omega=omega_f - n omega_v is close to zero, delta
omega/omega= K (2 delta alpha/alpha +0.5 delta mu/mu), K >>1, mu=m_p/m_e).
  The intervals between the levels are conveniently located in microwave
frequency range and the level widths are very small. Required accuracy of the
shift measurements is about 0.01-1 Hz. As examples, we consider molecules
Cl_2+, CuS, IrC, SiBr and HfF+.


title:
Jet modification and a comparative study of hadron v2 measurements in
  sqrt(s_NN) = 200 GeV Au+Au collisions at RHIC-PHENIX

abstract:
  In this analysis we measure the azimuthal angle($\phi$) dependence of hadrons
with respect to the reaction plane ($\Psi_{RP}$) in events that were triggered
by a high-$p_T$ $\pi^0$ of 5-10 GeV. Fitting the distribution of hadrons with a
function of the type $\xi(1+2v_2\cos{(2(\phi-\Psi_{RP})}))$, we observe that
there is no significant statistical difference between $v_2$ inclusive hadrons
and those hadrons from hard scattering events. We also compare the near-side
jet widths using PYTHIA simulations with $h^{\pm}$-$h^{\pm}$ correlations in
Au+Au at $\sqrt{s_{NN}}=200$ GeV.


title: Stellar Oscillations Network Group

abstract:
  Stellar Oscillations Network Group (SONG) is an initiative aimed at designing
and building a network of 1m-class telescopes dedicated to asteroseismology and
planet hunting. SONG will have 8 identical telescope nodes each equipped with a
high-resolution spectrograph and an iodine cell for obtaining precision radial
velocities and a CCD camera for guiding and imaging purposes. The main
asteroseismology targets for the network are the brightest (V<6) stars. In
order to improve performance and reduce maintenance costs the instrumentation
will only have very few modes of operation. In this contribution we describe
the motivations for establishing a network, the basic outline of SONG and the
expected performance.


title:
Two Dimensional Quantum Well of Gluons in Color Ferromagnetic Quark
  Matter

abstract:
  We have recently pointed out that color magnetic field is generated in dense
quark matter, i.e. color ferromagnetic phase of quark matter. Using light cone
quantization, we show that gluons occupying the lowest Landau level under the
color magnetic field effectively form a two dimensional quantum well (layer),
in which infinitely many zero modes of the gluons are present. We discuss that
the zero modes of the gluons form a quantum Hall state by interacting
repulsively with each other, just as electrons do in semiconductors. Such a
ferromagnetic quark matter with the layer structure of the gluons is a possible
origin of extremely strong magnetic field observed in magnetars.


title:
Une nouvelle condition d'independance pour le theoreme de la limite
  centrale

abstract:
  We prove a central limit theorem with aassumptions which are many weak than
classical conditions


title: High-Visibility Multi-Photon Interference of Classical Light

abstract:
  It is shown that the visibility of multi-photon interference for classical
sources grows rapidly with the order of interference. For three-photon and
four-photon interference of two coherent sources, the visibility can be as high
as 81.9% and 94.4%, respectively, - much higher than the 'classical limit' of
two-photon interference (50%). High-visibility three-photon and four-photon
interference has been observed in experiment, for both coherent and
pseudo-thermal light.


title: A discrete computer network model with expanding dimensions

abstract:
  Complex networks with expanding dimensions are studied, where the networks
may be directed and weighted, and network nodes are varying in discrete time in
the sense that some new nodes may be added and some old nodes may be removed
from time to time. A model of such networks in computer data transmission is
discussed. Each node on the network has fixed dimensionality, while the
dimension of the whole network is defined by the total number of nodes. Based
on the spectacular properties of data transmission on computer networks, some
new concepts of stable and unstable networks differing from the classical
Lyapunov stability are defined. In particular, a special unstable network
model, called devil network, is introduced and discussed. It is further found
that a variety of structures and connection weights affects the network
stability substantially. Several criteria on stability, instability, and devil
network are established for a rather general class of networks, where some
conditions are actually necessary and sufficient. Mathematically, this paper
makes a first attempt to rigorously formulate a fundamental issue of modeling
discrete linear time-varying systems with expanding dimensions and study their
basic stability property.


title: The Multiobjective Optimization of a Prismatic Drive

abstract:
  The multiobjective optimization of Slide-o-Cam is reported in this paper.
Slide-o-Cam is a cam mechanism with multiple rollers mounted on a common
translating follower. This transmission provides pure-rolling motion, thereby
reducing the friction of rack-and-pinions and linear drives. A Pareto frontier
is obtained by means of multiobjective optimization. This optimization is based
on three objective functions: (i) the pressure angle, which is a suitable
performance index for the transmission because it determines the amount of
force transmitted to the load vs. that transmitted to the machine frame; (ii)
the Hertz pressure used to evaluate the stresses produced on the contact
surface between cam and roller; and (iii) the size of the mechanism,
characterized by the number of cams and their width.


title: Environment Dependent Charge Potential for Water

abstract:
  We present a new interatomic potential for water captured in a
charge-transfer embedded atom method (EAM) framework. The potential accounts
for explicit, dynamical charge transfer in atoms as a function of the local
chemical environment. As an initial test of the charge-transfer EAM approach
for a molecular system, we have constructed a relatively simple version of the
potential and examined its ability to model the energetics of small water
clusters. The excellent agreement between our results and current experimental
and higher-level quantum computational data signifies a successful first step
towards developing a unified charge-transfer potential capable of accurately
describing the polymorphs, dynamics, and complex thermodynamic behavior of
water.


title: A real convexity theorem for quasi-hamiltonian actions

abstract:
  The main result of this paper is a quasi-hamiltonian analogue of a special
case of the O'Shea-Sjamaar convexity theorem for usual momentum maps. We denote
by U a simply connected compact connected Lie group and we fix an involutive
automorphism of maximal rank on this Lie group (such an automorphism always
exists). We then denote by M a quasi-hamiltonian U-space and we prove that the
image under the momentum map of the fixed-point set of a form-reversing
compatible involution of M is a convex polytope, which is in fact equal to the
full momentum polytope. This theorem was announced in arXiv:math/0609517v1. As
an application, we obtain an example of lagrangian subspace in representation
spaces of surface groups.


title: Coherent dynamics of photoinduced nucleation processes

abstract:
  We study the dynamics of initial nucleation processes of photoinduced
structural change of molecular crystals. In order to describe the nonadiabatic
transition in each molecule, we employ a model of localized electrons coupled
with a fully quantized phonon mode, and the time-dependent Schr\"odinger
equation for the model is numerically solved. We found a minimal model to
describe the nucleation induced by injection of an excited state of a single
molecule in which multiple types of intermolecular interactions are required.
In this model coherently driven molecular distortion plays an important role in
the successive conversion of electronic states which leads to photoinduced
cooperative phenomena.


title: Models of Neutrino Masses and Mixings: a Progress Report

abstract:
  We present some recent developments on model building for neutrino masses and
mixings. In particular, we review tri-bimaximal neutrino mixing derived from
discrete groups, notably A4. We discuss the problems encountered with extending
the symmetry to the quark sector and with Grand Unification.


title: Even parity excitations of the nucleon in lattice QCD

abstract:
  We study the spectrum of the even parity excitations of the nucleon in
quenched lattice QCD. We extend our earlier analysis by including an expanded
basis of nucleon interpolating fields, increasing the physical size of the
lattice, including more configurations to enhance statistics and probing closer
to the chiral limit. With a review of world lattice data, we conclude that
there is little evidence of the Roper resonance in quenched lattice QCD.


title:
Spectrum generating algebras for position-dependent mass oscillator
  Schrodinger equations

abstract:
  The interest of quadratic algebras for position-dependent mass Schr\"odinger
equations is highlighted by constructing spectrum generating algebras for a
class of d-dimensional radial harmonic oscillators with $d \ge 2$ and a
specific mass choice depending on some positive parameter $\alpha$. Via some
minor changes, the one-dimensional oscillator on the line with the same kind of
mass is included in this class. The existence of a single unitary irreducible
representation belonging to the positive-discrete series type for $d \ge 2$ and
of two of them for d=1 is proved. The transition to the constant-mass limit
$\alpha \to 0$ is studied and deformed su(1,1) generators are constructed.
These operators are finally used to generate all the bound-state wavefunctions
by an algebraic procedure.


abstract:
  We consider exact and quasi-exact solvability of the one-dimensional
Fokker-Planck equation based on the connection between the Fokker-Planck
equation and the Schr\"odinger equation. A unified consideration of these two
types of solvability is given from the viewpoint of prepotential together with
Bethe ansatz equations. Quasi-exactly solvable Fokker-Planck equations related
to the $sl(2)$-based systems in Turbiner's classification are listed. We also
present one $sl(2)$-based example which is not listed in Turbiner's scheme.

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


title: Tuning the shape of semiconductor microstadium laser

abstract:
  We presented a detailed experimental study on lasing in GaAs microstadium
with various shapes. Unlike most deformed microcavities, the lasing threshold
varies non-monotonically with the major-to-minor-axis ratio of the stadium.
Under spatially uniform optical pumping, the first lasing mode corresponds to a
high-quality scar mode consisting of several unstable periodic orbits. By
tuning the shape of GaAs stadium, we are able to minimize the lasing threshold.
This work demonstrates the possibility of controlling chaotic microcavity
laser.


title: Gauge Mediation with D-term SUSY Breaking

abstract:
  We construct a gauge-mediation model with a D-term supersymmetry (SUSY)
breaking. R-symmetry breaking necessary for generating the SUSY standard-model
gaugino masses is given by gaugino condensation of a strongly coupled gauge
theory in the hidden sector. The energy scale of the strong dynamics of the
hidden sector gauge theory should be around the messenger mass scale M, or
otherwise perturbative calculations would be reliable and would lead to
negative soft mass squared for squarks and sleptons. Thus, all the mass scales
are controlled by a virtually single parameter, \sqrt{D}/M. This model covers a
very wide range of gravitino mass, m_{3/2} \simeq 1 eV--100 TeV. Possible
embeddings of the model in string theory are also discussed.


title:
Infinite loop superalgebras of the Dirac theory on the Euclidean
  Taub-NUT space

abstract:
  The Dirac theory in the Euclidean Taub-NUT space gives rise to a large
collection of conserved operators associated to genuine or hidden symmetries.
They are involved in interesting algebraic structures as dynamical algebras or
even infinite-dimensional algebras or superalgebras. One presents here the
infinite-dimensional superalgebra specific to the Dirac theory in manifolds
carrying the Gross-Perry-Sorkin monopole. It is shown that there exists an
infinite-dimensional superalgebra that can be seen as a twisted loop
superalgebra.


title: Poisson approximation for non-backtracking random walks

abstract:
  Random walks on expander graphs were thoroughly studied, with the important
motivation that, under some natural conditions, these walks mix quickly and
provide an efficient method of sampling the vertices of a graph. Alon,
Benjamini, Lubetzky and Sodin studied non-backtracking random walks on regular
graphs, and showed that their mixing rate may be up to twice as fast as that of
the simple random walk. As an application, they showed that the maximal number
of visits to a vertex, made by a non-backtracking random walk of length $n$ on
a high-girth $n$-vertex regular expander, is typically $(1+o(1))\frac{\log
n}{\log\log n}$, as in the case of the balls and bins experiment. They further
asked whether one can establish the precise distribution of the visits such a
walk makes.
  In this work, we answer the above question by combining a generalized form of
Brun's sieve with some extensions of the ideas in Alon et al. Let $N_t$ denote
the number of vertices visited precisely $t$ times by a non-backtracking random
walk of length $n$ on a regular $n$-vertex expander of fixed degree and girth
$g$. We prove that if $g=\omega(1)$, then for any fixed $t$, $N_t/n$ is
typically $\frac{1}{\mathrm{e}t!}+o(1)$. Furthermore, if $g=\Omega(\log\log
n)$, then $N_t/n$ is typically $\frac{1+o(1)}{\mathrm{e}t!}$ uniformly on all
$t \leq (1-o(1))\frac{\log n}{\log\log n}$ and 0 for all $t \geq
(1+o(1))\frac{\log n}{\log\log n}$. In particular, we obtain the above result
on the typical maximal number of visits to a single vertex, with an improved
threshold window. The essence of the proof lies in showing that variables
counting the number of visits to a set of sufficiently distant vertices are
asymptotically independent Poisson variables.


title: Demixing and orientational ordering in mixtures of rectangular particles

abstract:
  Using scaled-particle theory for binary mixtures of two-dimensional hard
particles with rotational freedom, we analyse the stability of nematic phases
and the demixing phase behaviour of a variety of mixtures, focussing on cases
where at least one of the components consists of hard rectangles or hard
squares. A pure fluid of hard rectangles may exhibit, aside from the usual
uniaxial nematic phase, an additional (tetratic) oriented phase, possessing two
directors, which is the analogue of the biaxial or cubatic phases in three-
dimensional fluids. There is computer simulation evidence that the tetratic
phase might be stable with respect to phases with spatial order for rectangles
with low aspect ratios. As hard rectangles are mixed with other particles not
possessing stable tetratic order by themselves, the tetratic phase is
destabilised, via a first- or second-order phase transition, to uniaxial
nematic or isotropic phases; for hard rectangles of low aspect ratio tetratic
order persists in a relatively large range of volume fractions. The order of
these transitions depends on the particle geometry, dimensions and
thermodynamic conditions of the mixture. The second component of the mixture
has been chosen to be hard discs or disco-rectangles, the geometry of which is
different from that of rectangles, leading to packing frustration and demixing
behaviour, or simply rectangles of different aspect ratio. These mixtures may
be good candidates for observing thermodynamically stable tetratic phases in
monolayers of hard particles. Finally, demixing between fluid
(isotropic--tetratic or tetratic--tetratic) phases is seen to occur in mixtures
of hard squares of different sizes when the size ratio is sufficiently large.


title: Wave interference effect on polymer microstadium laser

abstract:
  We investigate the lasing modes in fully chaotic polymer microstadiums under
optical pumping. The lasing modes are regularly spaced in frequency, and their
amplitudes oscillate with frequency. Our numerical simulations reveal that the
lasing modes are multi-orbit scar modes. The interference of partial waves
propagating along the constituent orbits results in local maxima of quality
factor at certain frequencies. The observed modulation of lasing mode amplitude
with frequency results from the variation of quality factor, which provides the
direct evidence of wave interference effect in open chaotic microcavities.


title: THz emission from ultrafast optical orientation

abstract:
  We show both theoretically and experimentally that the magnetization density
accompanying ultrafast excitation of a semiconductor with circular polarized
light varies rapidly enough to produce a detectable THz field.


title: Unitarity analysis of a non-Abelian gauge invariant action with a mass

abstract:
  In previous work done by us and coworkers, we have been able to construct a
local, non-Abelian gauge invariant action with a mass parameter, based on the
nonlocal gauge invariant mass dimension two operator F1/D^2F. The
renormalizability of the resulting action was proven to all orders of
perturbation theory, in the class of linear covariant gauges. We also discussed
the perturbative equivalence of the model with ordinary massless Yang-Mills
gauge theories when the mass is identically zero. Furthermore, we pointed out
the existence of a BRST symmetry with corresponding nilpotent charge. In this
paper, we study the issue of unitarity of this massive gauge model. Firstly, we
provide a short review how to discuss the unitarity making use of the BRST
charge. Afterwards we make a detailed study of the most general version of our
action, and we come to the conclusion that the model is not unitary, as we are
unable to remove all the negative norm states from the physical spectrum in a
consistent way.


title:
Relativistic Tennis with Photons: Demonstration of Frequency Upshifting
  by a Relativistic Flying Mirror through Two Colliding Laser Pulses

abstract:
  Since the advent of chirped pulse amplification1 the peak power of lasers has
grown dramatically and opened the new branch of high field science, delivering
the focused irradiance, electric fields of which drive electrons into the
relativistic regime. In a plasma wake wave generated by such a laser,
modulations of the electron density naturally and robustly take the shape of
paraboloidal dense shells, separated by evacuated regions, moving almost at the
speed of light. When we inject another counter-propagating laser pulse, it is
partially reflected from the shells, acting as relativistic flying
(semi-transparent) mirrors, producing an extremely time-compressed
frequency-multiplied pulse which may be focused tightly to the diffraction
limit. This is as if the counterstreaming laser pulse bounces off a
relativistically swung tennis racket, turning the ball of the laser photons
into another ball of coherent X-ray photons but with a form extremely
relativistically compressed to attosecond and zeptosecond levels. Here we
report the first demonstration of the frequency multiplication detected from
the reflection of a weak laser pulse in the region of the wake wave generated
by the driver pulse in helium plasma. This leads to the possibility of very
strong pulse compression and extreme coherent light intensification. This
Relativistic Tennis with photon beams is demonstrated leading to the
possibility toward reaching enormous electromagnetic field intensification and
finally approaching the Schwinger field, toward which the vacuum nonlinearly
warps and eventually breaks, producing electron-positron pairs.


title: Modelling long-term trends in lunar exposure to the Earth's plasmasheet

abstract:
  This paper shows how the exposure of the Moon to the Earth's plasmasheet is
subject to decadal variations due to lunar precession. The latter is a key
property of the Moon's apparent orbit around the Earth - the nodes of that
orbit precess around the ecliptic, completing one revolution every 18.6 years.
This precession is responsible for a number of astronomical phenomena, e.g. the
year to year drift of solar and lunar eclipse periods. It also controls the
ecliptic latitude at which the Moon crosses the magnetotail and thus the number
and duration of lunar encounters with the plasmasheet. This paper presents a
detailed model of those encounters and applies it to the period 1960 to 2030.
This shows that the total lunar exposure to the plasmasheet will vary from 10
hours per month at a minimum of the eighteen-year cycle rising to 40 hours per
month at the maximum. These variations could have a profound impact on the
accumulation of charge due plasmasheet electrons impacting the lunar surface.
Thus we should expect the level of lunar surface charging to vary over the
eighteen-year cycle. The literature contains reports that support this: several
observations made during the cycle maximum of 1994-2000 are attributed to
bombardment and charging of the lunar surface by plasmasheet electrons. Thus we
conclude that lunar surface charging will vary markedly over an eighteen-year
cycle driven by lunar precession. It is important to interpret lunar
environment measurements in the context of this cycle and to allow for the
cycle when designing equipment for deployment on the lunar surface. This is
particularly important in respect of developing plans for robotic exploration
on the lunar surface during the next cycle maximum of 2012-19.


title: The Witten-Reshetikhin-Turaev Invariants of Lens Spaces

abstract:
  We derive an explicit formula for the Witten-Reshetikhin-Turaev
SO(3)-invariants of lens spaces. We use the representation of the mapping class
group of the torus corresponding to the Witten-Reshetikhin-Turaev SO(3)-TQFT to
give such formula.


title:
Synchronization of Excitatory Neurons with Strongly Heterogeneous Phase
  Responses

abstract:
  In many real-world oscillator systems, the phase response curves are highly
heterogeneous. However, dynamics of heterogeneous oscillator networks has not
been seriously addressed. We propose a theoretical framework to analyze such a
system by dealing explicitly with the heterogeneous phase response curves. We
develop a novel method to solve the self-consistent equations for order
parameters by using formal complex-valued phase variables, and apply our theory
to networks of in vitro cortical neurons. We find a novel state transition that
is not observed in previous oscillator network models.


title:
Comment on `Intrinsic tunnelling spectroscopy of
  Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$: The junction-size dependence of
  self-heating'[Phys.Rev.B 73, 224501 (2006)]

abstract:
  The recent PRB 73, 224501 (2006) henceforth referred as Ref.\cite{0} asserts
that self-heating decreases with sample area reduction and claims to identify
the intrinsic cause of ITS in submicrometre `mesa'. I will show that this
assertion lacks substantiation. I will further demonstrate that one and the
same $R(T)$ and the parameter-free Newton's Law of Cooling describe
quantitatively a rich variety of ITS behaviours taken by Ref.\cite{0} above and
below $T_c$ at bath temperatures spanned over 150K. Thus this finding presents
strong evidence in favour of heating as the cause of the `intrinsic tunnelling
spectra' (ITS) promoted by Ref.\cite{0}.


title:
Dependence of CMI Growth Rates on Electron Velocity Distributions and
  Perturbation by Solitary Waves

abstract:
  We calculate growth rates and corresponding gains for RX and LO mode
radiation associated with the cyclotron maser instability for parameterized
horseshoe electron velocity distributions. The velocity distribution function
was modeled to closely fit the electron distribution functions observed in the
auroral cavity. We systematically varied the model parameters as well as the
propagation direction to study the dependence of growth rates on model
parameters. The growth rate depends strongly on loss cone opening angle, which
must be less than $90^{o}$ for significant CMI growth. The growth rate is
sharply peaked for perpendicular radiation ($k_{\parallel} = 0$), with a
full-width at half-maximum $1.7^{o}$, in good agreement with observed k-vector
orientations and numerical simulations. The fractional bandwidth varied between
10$^{-4}$ and 10$^{-2}$, depending most strongly on propagation direction. This
range encompasses nearly all observed fractional AKR burst bandwidths. We find
excellent agreement between the computed RX mode emergent intensities and
observed AKR intensities assuming convective growth length $L_c\approx$20-40 km
and group speed 0.15$c$. The only computed LO mode growth rates compatible
observed LO mode radiation levels occurred for number densities more than 100
times the average energetic electron densities measured in auroral cavities.
This implies that LO mode radiation is not produced directly by the CMI
mechanism but more likely results from mode conversion of RX mode radiation. We
find that perturbation of the model velocity distribution by large ion solitary
waves (ion holes) can enhance the growth rate by a factor of 2-4. This will
result in a gain enhancement more than 40 dB depending on the convective growth
length within the structure. Similar enhancements may be caused by EMIC waves.