77 research outputs found
Two interacting diffusing particles on low-dimensional discrete structures
In this paper we study the motion of two particles diffusing on
low-dimensional discrete structures in presence of a hard-core repulsive
interaction. We show that the problem can be mapped in two decoupled problems
of single particles diffusing on different graphs by a transformation we call
'diffusion graph transform'. This technique is applied to study two specific
cases: the narrow comb and the ladder lattice. We focus on the determination of
the long time probabilities for the contact between particles and their
reciprocal crossing. We also obtain the mean square dispersion of the particles
in the case of the narrow comb lattice. The case of a sticking potential and of
'vicious' particles are discussed.Comment: 9 pages, 6 postscript figures, to appear in 'Journal of Physics
A',-January 200
Classical diffusion of N interacting particles in one dimension: General results and asymptotic laws
I consider the coupled one-dimensional diffusion of a cluster of N classical
particles with contact repulsion. General expressions are given for the
probability distributions, allowing to obtain the transport coefficients. In
the limit of large N, and within a gaussian approximation, the diffusion
constant is found to behave as N^{-1} for the central particle and as (\ln
N)^{-1} for the edge ones. Absolute correlations between the edge particles
increase as (\ln N)^{2}. The asymptotic one-body distribution is obtained and
discussed in relation of the statistics of extreme events.Comment: 6 pages, 2 eps figure
Analysis of self--averaging properties in the transport of particles through random media
We investigate self-averaging properties in the transport of particles
through random media. We show rigorously that in the subdiffusive anomalous
regime transport coefficients are not self--averaging quantities. These
quantities are exactly calculated in the case of directed random walks. In the
case of general symmetric random walks a perturbative analysis around the
Effective Medium Approximation (EMA) is performed.Comment: 4 pages, RevTeX , No figures, submitted to Physical Review E (Rapid
Communication
Anomalous diffusion, Localization, Aging and Sub-aging effects in trap models at very low temperature
We study in details the dynamics of the one dimensional symmetric trap model,
via a real-space renormalization procedure which becomes exact in the limit of
zero temperature. In this limit, the diffusion front in each sample consists in
two delta peaks, which are completely out of equilibrium with each other. The
statistics of the positions and weights of these delta peaks over the samples
allows to obtain explicit results for all observables in the limit .
We first compute disorder averages of one-time observables, such as the
diffusion front, the thermal width, the localization parameters, the
two-particle correlation function, and the generating function of thermal
cumulants of the position. We then study aging and sub-aging effects : our
approach reproduces very simply the two different aging exponents and yields
explicit forms for scaling functions of the various two-time correlations. We
also extend the RSRG method to include systematic corrections to the previous
zero temperature procedure via a series expansion in . We then consider the
generalized trap model with parameter and obtain that the
large scale effective model at low temperature does not depend on in
any dimension, so that the only observables sensitive to are those
that measure the `local persistence', such as the probability to remain exactly
in the same trap during a time interval. Finally, we extend our approach at a
scaling level for the trap model in and obtain the two relevant time
scales for aging properties.Comment: 33 pages, 3 eps figure
Driven Tunneling Dynamics: Bloch-Redfield Theory versus Path Integral Approach
In the regime of weak bath coupling and low temperature we demonstrate
numerically for the spin-boson dynamics the equivalence between two widely used
but seemingly different roads of approximation, namely the path integral
approach and the Bloch-Redfield theory. The excellent agreement between these
two methods is corroborated by a novel efficient analytical high-frequency
approach: it well approximates the decay of quantum coherence via a series of
damped coherent oscillations. Moreover, a suitably tuned control field can
selectively enhance or suppress quantum coherence.Comment: 4 pages including 3 figures, submitted for publicatio
Cumulant Expansions and the Spin-Boson Problem
The dynamics of the dissipative two-level system at zero temperature is
studied using three different cumulant expansion techniques. The relative
merits and drawbacks of each technique are discussed. It is found that a new
technique, the non-crossing cumulant expansion, appears to embody the virtues
of the more standard cumulant methods.Comment: 26 pages, LaTe
Random walk on Bethe lattice and hyperbolic geometry
We give the exact solution to the problem of a random walk on the Bethe
lattice through a mapping on an asymmetric random walk on the half-line. We
also study the continuous limit of this model, and discuss in detail the
relation between the random walk on the Bethe lattice and Brownian motion on a
space of constant negative curvature.Comment: 12 pages. Revised version (minor changes) to appear in J. Phys.
Quantum dynamics in strong fluctuating fields
A large number of multifaceted quantum transport processes in molecular
systems and physical nanosystems can be treated in terms of quantum relaxation
processes which couple to one or several fluctuating environments. A thermal
equilibrium environment can conveniently be modelled by a thermal bath of
harmonic oscillators. An archetype situation provides a two-state dissipative
quantum dynamics, commonly known under the label of a spin-boson dynamics. An
interesting and nontrivial physical situation emerges, however, when the
quantum dynamics evolves far away from thermal equilibrium. This occurs, for
example, when a charge transferring medium possesses nonequilibrium degrees of
freedom, or when a strong time-dependent control field is applied externally.
Accordingly, certain parameters of underlying quantum subsystem acquire
stochastic character. Herein, we review the general theoretical framework which
is based on the method of projector operators, yielding the quantum master
equations for systems that are exposed to strong external fields. This allows
one to investigate on a common basis the influence of nonequilibrium
fluctuations and periodic electrical fields on quantum transport processes.
Most importantly, such strong fluctuating fields induce a whole variety of
nonlinear and nonequilibrium phenomena. A characteristic feature of such
dynamics is the absence of thermal (quantum) detailed balance.Comment: review article, Advances in Physics (2005), in pres
Random walks and polymers in the presence of quenched disorder
After a general introduction to the field, we describe some recent results
concerning disorder effects on both `random walk models', where the random walk
is a dynamical process generated by local transition rules, and on `polymer
models', where each random walk trajectory representing the configuration of a
polymer chain is associated to a global Boltzmann weight. For random walk
models, we explain, on the specific examples of the Sinai model and of the trap
model, how disorder induces anomalous diffusion, aging behaviours and Golosov
localization, and how these properties can be understood via a strong disorder
renormalization approach. For polymer models, we discuss the critical
properties of various delocalization transitions involving random polymers. We
first summarize some recent progresses in the general theory of random critical
points : thermodynamic observables are not self-averaging at criticality
whenever disorder is relevant, and this lack of self-averaging is directly
related to the probability distribution of pseudo-critical temperatures
over the ensemble of samples of size . We describe the
results of this analysis for the bidimensional wetting and for the
Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S.,
France, November 200
Hellmann-Feynman theorem and fluctuation-correlation analysis of the Calogero-Sutherland model
Exploiting the results of the exact solution for the ground state of the
one-dimensional spinless quantum gas of Fermions and impenetrable Bosons with
the mu/x_{ij}^2 particle-particle interaction, the Hellmann-Feynman theorem
yields mutually compensating divergences of both the kinetic and the
interaction energy in the limiting case mu to -1/4. These divergences result
from the peculiar behavior of both the momentum distribution (for large
momenta) and the pair density (for small inter-particle separation). The
available analytical pair densities for mu=-1/4, 0, and 2 allow to analyze
particle-number fluctuations. They are suppressed by repulsive interaction
(mu>0), enhanced by attraction (mu<0), and may therefore measure the kind and
strength of correlation. Other recently proposed purely quantum-kinematical
measures of the correlation strength arise from the small-separation behavior
of the pair density or - for Fermions - from the non-idempotency of the
momentum distribution and its large-momenta behavior. They are compared with
each other and with reference-free, short-range correlation-measuring ratios of
the kinetic and potential energies.Comment: 30 pages, 9 figures, revised version, short version appeared as PRB
62, 15279-15282 (2000
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