505 research outputs found
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
Persistent Current of Free Electrons in the Plane
Predictions of Akkermans et al. are essentially changed when the Krein
spectral displacement operator is regularized by means of zeta function.
Instead of piecewise constant persistent current of free electrons on the plane
one has a current which varies linearly with the flux and is antisymmetric with
regard to all time preserving values of including . Different
self-adjoint extensions of the problem and role of the resonance are discussed.Comment: (Comment on "Relation between Persistent Currents and the Scattering
Matrix", Phys. Rev. Lett. {\bf 66}, 76 (1991)) plain latex, 4pp., IPNO/TH
94-2
Passive Sliders on Fluctuating Surfaces: Strong-Clustering States
We study the clustering properties of particles sliding downwards on a
fluctuating surface evolving through the Kardar-Parisi-Zhang equation, a
problem equivalent to passive scalars driven by a Burgers fluid. Monte Carlo
simulations on a discrete version of the problem in one dimension reveal that
particles cluster very strongly: the two point density correlation function
scales with the system size with a scaling function which diverges at small
argument. Analytic results are obtained for the Sinai problem of random walkers
in a quenched random landscape. This equilibrium system too has a singular
scaling function which agrees remarkably with that for advected particles.Comment: To be published in Physical Review Letter
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
Explicit formulae in probability and in statistical physics
We consider two aspects of Marc Yor's work that have had an impact in
statistical physics: firstly, his results on the windings of planar Brownian
motion and their implications for the study of polymers; secondly, his theory
of exponential functionals of Levy processes and its connections with
disordered systems. Particular emphasis is placed on techniques leading to
explicit calculations.Comment: 14 pages, 2 figures. To appear in Seminaire de Probabilites, Special
Issue Marc Yo
Arithmetic area for m planar Brownian paths
We pursue the analysis made in [1] on the arithmetic area enclosed by m
closed Brownian paths. We pay a particular attention to the random variable
S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also
called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm
times by path m. Various results are obtained in the asymptotic limit
m->infinity. A key observation is that, since the paths are independent, one
can use in the m paths case the SLE information, valid in the 1-path case, on
the 0-winding sectors arithmetic area.Comment: 12 pages, 2 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
Hall Conductivity for Two Dimensional Magnetic Systems
A Kubo inspired formalism is proposed to compute the longitudinal and
transverse dynamical conductivities of an electron in a plane (or a gas of
electrons at zero temperature) coupled to the potential vector of an external
local magnetic field, with the additional coupling of the spin degree of
freedom of the electron to the local magnetic field (Pauli Hamiltonian). As an
example, the homogeneous magnetic field Hall conductivity is rederived. The
case of the vortex at the origin is worked out in detail. This system happens
to display a transverse Hall conductivity ( breaking effect) which is
subleading in volume compared to the homogeneous field case, but diverging at
small frequency like . A perturbative analysis is proposed for the
conductivity in the random magnetic impurity problem (Poissonian vortices in
the plane). At first order in perturbation theory, the Hall conductivity
displays oscillations close to the classical straight line conductivity of the
mean magnetic field.Comment: 28 pages, latex, 2 figure
On the harmonic oscillator on the Lobachevsky plane
We introduce the harmonic oscillator on the Lobachevsky plane with the aid of
the potential where is the curvature
radius and is the geodesic distance from a fixed center. Thus the potential
is rotationally symmetric and unbounded likewise as in the Euclidean case. The
eigenvalue equation leads to the differential equation of spheroidal functions.
We provide a basic numerical analysis of eigenvalues and eigenfunctions in the
case when the value of the angular momentum, , equals 0.Comment: to appear in Russian Journal of Mathematical Physics (memorial volume
in honor of Vladimir Geyler
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