2,094 research outputs found
Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries
We consider a driven diffusive system with two types of particles, A and B,
coupled at the ends to reservoirs with fixed particle densities. To define
stochastic dynamics that correspond to boundary reservoirs we introduce
projection measures. The stationary state is shown to be approached dynamically
through an infinite reflection of shocks from the boundaries. We argue that
spontaneous symmetry breaking observed in similar systems is due to placing
effective impurities at the boundaries and therefore does not occur in our
system. Monte-Carlo simulations confirm our results.Comment: 24 pages, 7 figure
Stochastic pump of interacting particles
We consider the overdamped motion of Brownian particles, interacting via
particle exclusion, in an external potential that varies with time and space.
We show that periodic potentials that maintain specific position-dependent
phase relations generate time-averaged directed current of particles. We obtain
analytic results for a lattice version of the model using a recently developed
perturbative approach. Many interesting features like particle-hole symmetry,
current reversal with changing density, and system-size dependence of current
are obtained. We propose possible experiments to test our predictions.Comment: 4 pages, 2 figure
Solution of a class of one-dimensional reaction-diffusion models in disordered media
We study a one-dimensional class of reaction-diffusion models on a
parameters manifold. The equations of motion of the correlation
functions close on this manifold. We compute exactly the long-time behaviour of
the density and correlation functions for
{\it quenched} disordered systems. The {\it quenched} disorder consists of
disconnected domains of reaction. We first consider the case where the disorder
comprizes a superposition, with different probabilistic weights, of finite
segments, with {\it periodic boundary conditions}. We then pass to the case of
finite segments with {\it open boundary conditions}: we solve the ordered
dynamics on a open lattice with help of the Dynamical Matrix Ansatz (DMA) and
investigate further its disordered version.Comment: 11 pages, no figures. To appear in Phys.Rev.
Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
We obtain exact travelling wave solutions for three families of stochastic
one-dimensional nonequilibrium lattice models with open boundaries. These
solutions describe the diffusive motion and microscopic structure of (i) of
shocks in the partially asymmetric exclusion process with open boundaries, (ii)
of a lattice Fisher wave in a reaction-diffusion system, and (iii) of a domain
wall in non-equilibrium Glauber-Kawasaki dynamics with magnetization current.
For each of these systems we define a microscopic shock position and calculate
the exact hopping rates of the travelling wave in terms of the transition rates
of the microscopic model. In the steady state a reversal of the bias of the
travelling wave marks a first-order non-equilibrium phase transition, analogous
to the Zel'dovich theory of kinetics of first-order transitions. The stationary
distributions of the exclusion process with shocks can be described in
terms of -dimensional representations of matrix product states.Comment: 27 page
Exclusion process for particles of arbitrary extension: Hydrodynamic limit and algebraic properties
The behaviour of extended particles with exclusion interaction on a
one-dimensional lattice is investigated. The basic model is called -ASEP
as a generalization of the asymmetric exclusion process (ASEP) to particles of
arbitrary length . Stationary and dynamical properties of the -ASEP
with periodic boundary conditions are derived in the hydrodynamic limit from
microscopic properties of the underlying stochastic many-body system. In
particular, the hydrodynamic equation for the local density evolution and the
time-dependent diffusion constant of a tracer particle are calculated. As a
fundamental algebraic property of the symmetric exclusion process (SEP) the
SU(2)-symmetry is generalized to the case of extended particles
Time-dependent correlation functions in a one-dimensional asymmetric exclusion process
We study a one-dimensional anisotropic exclusion process describing particles
injected at the origin, moving to the right on a chain of sites and being
removed at the (right) boundary. We construct the steady state and compute the
density profile, exact expressions for all equal-time n-point density
correlation functions and the time-dependent two-point function in the steady
state as functions of the injection and absorption rates. We determine the
phase diagram of the model and compare our results with predictions from
dynamical scaling and discuss some conjectures for other exclusion models.Comment: LATEX-file, 32 pages, Weizmann preprint WIS/93/01/Jan-P
Symmetric Exclusion Process with a Localized Source
We investigate the growth of the total number of particles in a symmetric
exclusion process driven by a localized source. The average total number of
particles entering an initially empty system grows with time as t^{1/2} in one
dimension, t/log(t) in two dimensions, and linearly in higher dimensions. In
one and two dimensions, the leading asymptotic behaviors for the average total
number of particles are independent on the intensity of the source. We also
discuss fluctuations of the total number of particles and determine the
asymptotic growth of the variance in one dimension.Comment: 7 pages; small corrections, references added, final versio
Reaction-controlled diffusion
The dynamics of a coupled two-component nonequilibrium system is examined by
means of continuum field theory representing the corresponding master equation.
Particles of species A may perform hopping processes only when particles of
different type B are present in their environment. Species B is subject to
diffusion-limited reactions. If the density of B particles attains a finite
asymptotic value (active state), the A species displays normal diffusion. On
the other hand, if the B density decays algebraically ~t^{-a} at long times
(inactive state), the effective attractive A-B interaction is weakened. The
combination of B decay and activated A hopping processes gives rise to
anomalous diffusion, with mean-square displacement ~ t^{1-a} for a
< 1. Such algebraic subdiffusive behavior ensues for n-th order B annihilation
reactions (n B -> 0) with n >=3, and n = 2 for d < 2. The mean-square
displacement of the A particles grows only logarithmically with time in the
case of B pair annihilation (n = 2) and d >= 2 dimensions. For radioactive B
decay (n = 1), the A particles remain localized. If the A particles may hop
spontaneously as well, or if additional random forces are present, the A-B
coupling becomes irrelevant, and conventional diffusion is recovered in the
long-time limit.Comment: 7 pages, revtex, no figures; latest revised versio
Diffusion-Annihilation in the Presence of a Driving Field
We study the effect of an external driving force on a simple stochastic
reaction-diffusion system in one dimension. In our model each lattice site may
be occupied by at most one particle. These particles hop with rates
to the right and left nearest neighbouring site resp. if this
site is vacant and annihilate with rate 1 if it is occupied. We show that
density fluctuations (i.e. the moments of the
density distribution at time ) do not depend on the spatial anisotropy
induced by the driving field, irrespective of the initial condition.
Furthermore we show that if one takes certain translationally invariant
averages over initial states (e.g. random initial conditions) even local
fluctuations do not depend on . In the scaling regime the
effect of the driving can be completely absorbed in a Galilei transformation
(for any initial condition). We compute the probability of finding a system of
sites in its stationary state at time if it was fully occupied at time
.Comment: 17 pages, latex, no figure
Exact solution of a one-parameter family of asymmetric exclusion processes
We define a family of asymmetric processes for particles on a one-dimensional
lattice, depending on a continuous parameter ,
interpolating between the completely asymmetric processes [1] (for ) and the n=1 drop-push models [2] (for ). For arbitrary \la,
the model describes an exclusion process, in which a particle pushes its right
neighbouring particles to the right, with rates depending on the number of
these particles. Using the Bethe ansatz, we obtain the exact solution of the
master equation .Comment: 14 pages, LaTe
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