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 $\mathfrak{g}$ be an untwisted affine Kac-Moody algebra over the field $K \,$, and let $U_q(\mathfrak{g})$ be the associated quantum enveloping algebra; let $\mathfrak{U}_q(g)$ be the Lusztig's integer form of $U_q(\mathfrak{g}) \,$, generated by $q$-divided powers of Chevalley generators over a suitable subring $R$ of $K(q) \,$. We prove a Poincar\'e-Birkhoff-Witt like theorem for $\mathfrak{U}_q(\mathfrak{g}) \,$, yielding a basis over $R$ made of ordered products of $q$-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 $n$-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 ($L\to\infty$), the distribution of the $n$-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 $V(x)=\phi(x)^2+\phi'(x)$). We study first the case of $\phi(x)$ being a white noise with zero mean. It is in particular shown that the ground state energy, which behaves on average like $\exp{-L^{1/3}}$ in agreement with previous work, is not a self averaging quantity in the limit $L\to\infty$ as is seen in the case of diagonal disorder. Then we consider the case when $\phi(x)$ has a non zero mean value.Comment: LaTeX, 33 pages, 9 figure

On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach

We consider a metric graph $\mathcal{G}$ made of two graphs $\mathcal{G}_1$ and $\mathcal{G}_2$ attached at one point. We derive a formula relating the spectral determinant of the Laplace operator $S_\mathcal{G}(\gamma)=\det(\gamma-\Delta)$ in terms of the spectral determinants of the two subgraphs. The result is generalized to describe the attachment of $n$ graphs. The formulae are also valid for the spectral determinant of the Schr\"odinger operator $\det(\gamma-\Delta+V(x))$.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

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

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