396 research outputs found
General flux to a trap in one and three dimensions
The problem of the flux to a spherical trap in one and three dimensions, for
diffusing particles undergoing discrete-time jumps with a given radial
probability distribution, is solved in general, verifying the Smoluchowski-like
solution in which the effective trap radius is reduced by an amount
proportional to the jump length. This reduction in the effective trap radius
corresponds to the Milne extrapolation length.Comment: Accepted for publication, in pres
Distribution of the Oscillation Period in the Underdamped One Dimensional Sinai Model
We consider the Newtonian dynamics of a massive particle in a one dimemsional
random potential which is a Brownian motion in space. This is the zero
temperature nondamped Sinai model. As there is no dissipation the particle
oscillates between two turning points where its kinetic energy becomes zero.
The period of oscillation is a random variable fluctuating from sample to
sample of the random potential. We compute the probability distribution of this
period exactly and show that it has a power law tail for large period, P(T)\sim
T^{-5/3} and an essential singluarity P(T)\sim \exp(-1/T) as T\to 0. Our exact
results are confirmed by numerical simulations and also via a simple scaling
argument.Comment: 9 pages LateX, 2 .eps figure
On the distribution of the Wigner time delay in one-dimensional disordered systems
We consider the scattering by a one-dimensional random potential and derive
the probability distribution of the corresponding Wigner time delay. It is
shown that the limiting distribution is the same for two different models and
coincides with the one predicted by random matrix theory. It is also shown that
the corresponding stochastic process is given by an exponential functional of
the potential.Comment: 11 pages, four references adde
Integer Partitions and Exclusion Statistics
We provide a combinatorial description of exclusion statistics in terms of
minimal difference partitions. We compute the probability distribution of
the number of parts in a random minimal partition. It is shown that the
bosonic point is a repulsive fixed point for which the limiting
distribution has a Gumbel form. For all positive the distribution is shown
to be Gaussian.Comment: 16 pages, 4 .eps figures include
A PBW basis for Lusztig's form of untwisted affine quantum groups
Let be an untwisted affine Kac-Moody algebra over the field
, and let be the associated quantum enveloping
algebra; let be the Lusztig's integer form of , generated by -divided powers of Chevalley
generators over a suitable subring of . We prove a
Poincar\'e-Birkhoff-Witt like theorem for ,
yielding a basis over made of ordered products of -divided powers of
suitable quantum root vectors.Comment: 22 pages, AMS-TeX C, Version 2.1c. This is the author's final
version, corresponding to the printed journal versio
Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap
Two random-walk related problems which have been studied independently in the
past, the expected maximum of a random walker in one dimension and the flux to
a spherical trap of particles undergoing discrete jumps in three dimensions,
are shown to be closely related to each other and are studied using a unified
approach as a solution to a Wiener-Hopf problem. For the flux problem, this
work shows that a constant c = 0.29795219 which appeared in the context of the
boundary extrapolation length, and was previously found only numerically, can
be derived explicitly. The same constant enters in higher-order corrections to
the expected-maximum asymptotics. As a byproduct, we also prove a new universal
result in the context of the flux problem which is an analogue of the Sparre
Andersen theorem proved in the context of the random walker's maximum.Comment: Two figs. Accepted for publication, Journal of Statistical Physic
Fotonima stimulirana desorpcija vodikovih iona iz poluvodičkih površina: dokazi izravnih i posrednih procesa
Photon-stimulated desorption of positive hydrogen ions from hydrogenated diamond and GaAs surfaces have been studied for incident photon energies around core-level binding energies of substrate atoms. In the case of diamond surfaces, the comparison between the H+ yield and the near edge X-ray absorption fine structure (NEXAFS) for electrons of selected kinetic energies reveals two different processes leading to photodesorption: an indirect process involving secondary electrons from the bulk and a direct process involving core-level excitations of surface carbon atoms bonded to hydrogen. The comparison of H+ photodesorption and electron photoemission as the function of photon energy from polar and non-polar GaAs surfaces provides clear evidence for direct desorption processes initiated by ionisation of corresponding core levels of bonding atoms.Proučavali smo fotonima stimuliranu desorpciju pozitivnih iona vodika iz hidrogeniziranih površina dijamanta i GaAs, za fotone energije oko energija vezanja unutarnjih elektrona atoma podloge. U slučaju površine dijamanta, usporedba prinosa H+ i fine strukture blizu-rubne apsorpcije X-zračenja (NEXAFS) za elektrone odabranih kinetičkih energija otkriva dva različita procesa koji uzrokuju fotodesorpciju: posredan proces uz sudjelovanje sekundarnih elektrona iz osnovnog materijala, i izravan proces uzrokovan uzbudom unutarnjih elektrona površinskih atoma ugljika vezanih na vodik. Usporedba fotodesorpcije H+ i emisije elektrona u ovisnosti o energiji fotona iz polarnih i nepolarnih površina GaAs daje jasne dokaze za izravne procese desorpcije uzrokovane ionizacijom odgovarajućih unutarnjih stanja veznih atoma
Universality of the Wigner time delay distribution for one-dimensional random potentials
We show that the distribution of the time delay for one-dimensional random
potentials is universal in the high energy or weak disorder limit. Our
analytical results are in excellent agreement with extensive numerical
simulations carried out on samples whose sizes are large compared to the
localisation length (localised regime). The case of small samples is also
discussed (ballistic regime). We provide a physical argument which explains in
a quantitative way the origin of the exponential divergence of the moments. The
occurence of a log-normal tail for finite size systems is analysed. Finally, we
present exact results in the low energy limit which clearly show a departure
from the universal behaviour.Comment: 4 pages, 3 PostScript figure
Universal Asymptotic Statistics of Maximal Relative Height in One-dimensional Solid-on-solid Models
We study the probability density function of the maximum relative
height in a wide class of one-dimensional solid-on-solid models of finite
size . For all these lattice models, in the large limit, a central limit
argument shows that, for periodic boundary conditions, takes a
universal scaling form , with the width of the fluctuating interface and the Airy
distribution function. For one instance of these models, corresponding to the
extremely anisotropic Ising model in two dimensions, this result is obtained by
an exact computation using transfer matrix technique, valid for any .
These arguments and exact analytical calculations are supported by numerical
simulations, which show in addition that the subleading scaling function is
also universal, up to a non universal amplitude, and simply given by the
derivative of the Airy distribution function .Comment: 13 pages, 4 figure
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