2,081 research outputs found
Schramm-Loewner Equations Driven by Symmetric Stable Processes
We consider shape, size and regularity of the hulls of the chordal
Schramm-Loewner evolution driven by a symmetric alpha-stable process. We obtain
derivative estimates, show that the complements of the hulls are Hoelder
domains, prove that the hulls have Hausdorff dimension 1, and show that the
trace is right-continuous with left limits almost surely.Comment: 22 pages, 4 figure
Stationary distributions for diffusions with inert drift
Consider reflecting Brownian motion in a bounded domain in that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential
Self-intersection local times of random walks: Exponential moments in subcritical dimensions
Fix , not necessarily integer, with . We study the -fold
self-intersection local time of a simple random walk on the lattice up
to time . This is the -norm of the vector of the walker's local times,
. We derive precise logarithmic asymptotics of the expectation of
for scales that are bounded from
above, possibly tending to zero. The speed is identified in terms of mixed
powers of and , and the precise rate is characterized in terms of
a variational formula, which is in close connection to the {\it
Gagliardo-Nirenberg inequality}. As a corollary, we obtain a large-deviation
principle for for deviation functions satisfying
t r_t\gg\E[\|\ell_t\|_p]. Informally, it turns out that the random walk
homogeneously squeezes in a -dependent box with diameter of order to produce the required amount of self-intersections. Our main tool is
an upper bound for the joint density of the local times of the walk.Comment: 15 pages. To appear in Probability Theory and Related Fields. The
final publication is available at springerlink.co
Stellar adiabatic mass loss model and applications
Roche-lobe overflow and common envelope evolution are very important in
binary evolution, which is believed to be the main evolutionary channel to hot
subdwarf stars. The details of these processes are difficult to model, but
adiabatic expansion provides an excellent approximation to the structure of a
donor star undergoing dynamical time scale mass transfer. We can use this model
to study the responses of stars of various masses and evolutionary stages as
potential donor stars, with the urgent goal of obtaining more accurate
stability criteria for dynamical mass transfer in binary population synthesis
studies. As examples, we describe here several models with the initial masses
equal to 1 Msun and 10 Msun, and identify potential limitations to the use of
our results for giant-branch stars.Comment: 7 pages, 5 figures,Accepted for publication in AP&SS, Special issue
Hot Sub-dwarf Stars, in Han Z., Jeffery S., Podsiadlowski Ph. ed
ECC2K-130 on NVIDIA GPUs
A major cryptanalytic computation is currently underway on multiple platforms, including standard CPUs, FPGAs, PlayStations and Graphics Processing Units (GPUs), to break the Certicom ECC2K-130 challenge. This challenge is to compute an elliptic-curve discrete logarithm on a Koblitz curve over . Optimizations have reduced the cost of the computation to approximately 277 bit operations in 261 iterations. GPUs are not designed for fast binary-field arithmetic; they are designed for highly vectorizable floating-point computations that fit into very small amounts of static RAM. This paper explains how to optimize the ECC2K-130 computation for this unusual platform. The resulting GPU software performs more than 63 million iterations per second, including 320 million multiplications per second, on a $500 NVIDIA GTX 295 graphics card. The same techniques for finite-field arithmetic and elliptic-curve arithmetic can be reused in implementations of larger systems that are secure against similar attacks, making GPUs an interesting option as coprocessors when a busy Internet server has many elliptic-curve operations to perform in parallel
The pseudogap state in superconductors: Extended Hartree approach to time-dependent Ginzburg-Landau Theory
It is well known that conventional pairing fluctuation theory at the Hartree
level leads to a normal state pseudogap in the fermionic spectrum. Our goal is
to extend this Hartree approximated scheme to arrive at a generalized mean
field theory of pseudogapped superconductors for all temperatures . While an
equivalent approach to the pseudogap has been derived elsewhere using a more
formal Green's function decoupling scheme, in this paper we re-interpret this
mean field theory and BCS theory as well, and demonstrate how they naturally
relate to ideal Bose gas condensation. Here we recast the Hartree approximated
Ginzburg-Landau self consistent equations in a T-matrix form. This recasting
makes it possible to consider arbitrarily strong attractive coupling, where
bosonic degrees of freedom appear at considerably above . The
implications for transport both above and below are discussed. Below
we find two types of contributions. Those associated with fermionic
excitations have the usual BCS functional form. That they depend on the
magnitude of the excitation gap, nevertheless, leads to rather atypical
transport properties in the strong coupling limit, where this gap (as distinct
from the order parameter) is virtually -independent. In addition, there are
bosonic terms arising from non-condensed pairs whose transport properties are
shown here to be reasonably well described by an effective time-dependent
Ginzburg-Landau theory.Comment: 14 pages, 5 figures, REVTeX4, submitted to PRB; clarification of the
diagrammatic technique added, one figure update
Test for entanglement using physically observable witness operators and positive maps
Motivated by the Peres-Horodecki criterion and the realignment criterion we
develop a more powerful method to identify entangled states for any bipartite
system through a universal construction of the witness operator. The method
also gives a new family of positive but non-completely positive maps of
arbitrary high dimensions which provide a much better test than the witness
operators themselves. Moreover, we find there are two types of positive maps
that can detect 2xN and 4xN bound entangled states. Since entanglement
witnesses are physical observables and may be measured locally our construction
could be of great significance for future experiments.Comment: 6 pages, 1 figure, revtex4 styl
Nucleon electroweak form factors in a meson-cloud model
The meson-cloud model of the nucleon consisting of a system of three valence
quarks surrounded by a meson cloud is applied to study the electroweak
structure of the proton and neutron. The electroweak nucleon form factors are
calculated within a light-front approach, by obtaining an overall good
description of the experimental data. Charge densities as a function of the
transverse distance with respect to the direction of the three-momentum
transfer are also discussed.Comment: Prepared for Proceedings of NSTAR2007, Workshop on the physics of
excited nucleons, Bonn (Germany), 5-8 September 200
The fermion dynamical symmetry model for the even--even and even--odd nuclei in the Xe--Ba region
The even--even and even--odd nuclei Xe-Xe and
Ba-Ba are shown to have a well-realized fermion dynamical symmetry. Their low-lying energy levels can be
described by a unified analytical expression with two (three) adjustable
parameters for even--odd (even--even) nuclei that is derived from the fermion
dynamical symmetry model. Analytical expressions are given for wavefunctions
and for transition rates that agree well with data. The distinction
between the FDSM and IBM limits is discussed. The experimentally
observed suppression of the the energy levels with increasing quantum
number can be explained as a perturbation of the pairing interaction on
the symmetry, which leads to an Pairing effect for nuclei.Comment: submitted to Phys. Rev. C, LaTeX, 31 pages, 8 figures with postscript
files available on request at [email protected]
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