1,776 research outputs found
Random Magnetic Impurities and the Landau Problem
The 2-dimensional density of states of an electron is studied for a
Poissonian random distribution of point vortices carrying flux in unit
of the quantum of flux. It is shown that, for any given density of impurities,
there is a transition, when , from an "almost free"
density of state -with only a depletion of states at the bottom of the spectrum
characterized by a Lifschitz tail- to a Landau density of state with sharp
Landau level oscillations. Several evidences and arguments for this transition
-numerical and analytical- are presented.Comment: 22 pages, latex, 4 figures upon reques
Excursions of diffusion processes and continued fractions
It is well-known that the excursions of a one-dimensional diffusion process
can be studied by considering a certain Riccati equation associated with the
process. We show that, in many cases of interest, the Riccati equation can be
solved in terms of an infinite continued fraction. We examine the probabilistic
significance of the expansion. To illustrate our results, we discuss some
examples of diffusions in deterministic and in random environments.Comment: 28 pages. Minor changes to Section
Exact Results on Sinai's Diffusion
We study the continuum version of Sinai's problem of a random walker in a
random force field in one dimension. A method of stochastic representations is
used to represent various probability distributions in this problem (mean
probability density function and first passage time distributions). This method
reproduces already known rigorous results and also confirms directly some
recent results derived using approximation schemes. We demonstrate clearly, in
the Sinai scaling regime, that the disorder dominates the problem and that the
thermal distributions tend to zero-one laws.Comment: 14 pages Latex. To appear J. Phys.
Localization Properties in One Dimensional Disordered Supersymmetric Quantum Mechanics
A model of localization based on the Witten Hamiltonian of supersymmetric
quantum mechanics is considered. The case where the superpotential is
a random telegraph process is solved exactly. Both the localization length and
the density of states are obtained analytically. A detailed study of the low
energy behaviour is presented. Analytical and numerical results are presented
in the case where the intervals over which is kept constant are
distributed according to a broad distribution. Various applications of this
model are considered.Comment: 43 pages, plain TEX, 8 figures not included, available upon request
from the Authors
Enumeration by kernel positions for strongly Bernoulli type truncation games on words
We find the winning strategy for a class of truncation games played on words.
As a consequence of the present author's recent results on some of these games
we obtain new formulas for Bernoulli numbers and polynomials of the second kind
and a new combinatorial model for the number of connected permutations of given
rank. For connected permutations, the decomposition used to find the winning
strategy is shown to be bijectively equivalent to King's decomposition, used to
recursively generate a transposition Gray code of the connected permutations
Products of random matrices and generalised quantum point scatterers
To every product of matrices, there corresponds a one-dimensional
Schr\"{o}dinger equation whose potential consists of generalised point
scatterers. Products of {\em random} matrices are obtained by making these
interactions and their positions random. We exhibit a simple one-dimensional
quantum model corresponding to the most general product of matrices in
. We use this correspondence to find new examples of
products of random matrices for which the invariant measure can be expressed in
simple analytical terms.Comment: 38 pages, 13 pdf figures. V2 : conclusion added ; Definition of
function change
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