472 research outputs found
Exact Asymptotic Results for Persistence in the Sinai Model with Arbitrary Drift
We obtain exact asymptotic results for the disorder averaged persistence of a
Brownian particle moving in a biased Sinai landscape. We employ a new method
that maps the problem of computing the persistence to the problem of finding
the energy spectrum of a single particle quantum Hamiltonian, which can be
subsequently found. Our method allows us analytical access to arbitrary values
of the drift (bias), thus going beyond the previous methods which provide
results only in the limit of vanishing drift. We show that on varying the
drift, the persistence displays a variety of rich asymptotic behaviors
including, in particular, interesting qualitative changes at some special
values of the drift.Comment: 17 pages, two eps figures (included
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
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
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
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
Individual energy level distributions for one-dimensional diagonal and off-diagonal disorder
We study the distribution of the -th energy level for two different
one-dimensional random potentials. This distribution is shown to be related to
the distribution of the distance between two consecutive nodes of the wave
function.
We first consider the case of a white noise potential and study the
distributions of energy level both in the positive and the negative part of the
spectrum. It is demonstrated that, in the limit of a large system
(), the distribution of the -th energy level is given by a
scaling law which is shown to be related to the extreme value statistics of a
set of independent variables.
In the second part we consider the case of a supersymmetric random
Hamiltonian (potential ). We study first the case of
being a white noise with zero mean. It is in particular shown that
the ground state energy, which behaves on average like in
agreement with previous work, is not a self averaging quantity in the limit
as is seen in the case of diagonal disorder. Then we consider the
case when has a non zero mean value.Comment: LaTeX, 33 pages, 9 figure
Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
We consider the totally asymmetric exclusion process in discrete time with
the parallel update. Constructing an appropriate transformation of the
evolution operator, we reduce the problem to that solvable by the Bethe ansatz.
The non-stationary solution of the master equation for the infinite 1D lattice
is obtained in a determinant form. Using a modified combinatorial treatment of
the Bethe ansatz, we give an alternative derivation of the resulting
determinant expression.Comment: 34 pages, 5 figures, final versio
On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach
We consider a metric graph made of two graphs
and attached at one point. We derive a formula relating the
spectral determinant of the Laplace operator
in terms of the spectral
determinants of the two subgraphs. The result is generalized to describe the
attachment of graphs. The formulae are also valid for the spectral
determinant of the Schr\"odinger operator .Comment: LaTeX, 8 pages, 7 eps figures, v2: new appendix, v3: discussions and
ref adde
Exponential Operators, Dobinski Relations and Summability
We investigate properties of exponential operators preserving the particle
number using combinatorial methods developed in order to solve the boson normal
ordering problem. In particular, we apply generalized Dobinski relations and
methods of multivariate Bell polynomials which enable us to understand the
meaning of perturbation-like expansions of exponential operators. Such
expansions, obtained as formal power series, are everywhere divergent but the
Pade summation method is shown to give results which very well agree with exact
solutions got for simplified quantum models of the one mode bosonic systems.Comment: Presented at XIIth Central European Workshop on Quantum Optics,
Bilkent University, Ankara, Turkey, 6-10 June 2005. 4 figures, 6 pages, 10
reference
New Shape Invariant Potentials in Supersymmetric Quantum Mechanics
Quantum mechanical potentials satisfying the property of shape invariance are
well known to be algebraically solvable. Using a scaling ansatz for the change
of parameters, we obtain a large class of new shape invariant potentials which
are reflectionless and possess an infinite number of bound states. They can be
viewed as q-deformations of the single soliton solution corresponding to the
Rosen-Morse potential. Explicit expressions for energy eigenvalues,
eigenfunctions and transmission coefficients are given. Included in our
potentials as a special case is the self-similar potential recently discussed
by Shabat and Spiridonov.Comment: 8pages, Te
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