608 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 $\phi(x)$ 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 $\phi(x)$ 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

### Random Aharonov-Bohm vortices and some funny families of integrals

A review of the random magnetic impurity model, introduced in the context of
the integer Quantum Hall effect, is presented. It models an electron moving in
a plane and coupled to random Aharonov-Bohm vortices carrying a fraction of the
quantum of flux. Recent results on its perturbative expansion are given. In
particular, some funny families of integrals show up to be related to the
Riemann $\zeta(3)$ and $\zeta(2)$.Comment: 10 page

### 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

### 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

### 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 $\alpha$ including $1/2$. 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

### Directed Random Walk on the Lattices of Genus Two

The object of the present investigation is an ensemble of self-avoiding and
directed graphs belonging to eight-branching Cayley tree (Bethe lattice)
generated by the Fucsian group of a Riemann surface of genus two and embedded
in the Pincar\'e unit disk. We consider two-parametric lattices and calculate
the multifractal scaling exponents for the moments of the graph lengths
distribution as functions of these parameters. We show the results of numerical
and statistical computations, where the latter are based on a random walk
model.Comment: 17 pages, 8 figure

### 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

### Comment on "Statistical Mechanics of Non-Abelian Chern-Simons Particles"

The second virial coefficient for non-Abelian Chern-Simons particles is
recalculated. It is shown that the result is periodic in the flux parameter
just as in the Abelian theory.Comment: 3 pages, latex fil

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