152 research outputs found
Exact Solution of an Exclusion Model in the Presence of a moving Impurity
We study a recently introduced model which consists of positive and negative
particles on a ring. The positive (negative) particles hop clockwise
(counter-clockwise) with rate 1 and oppositely charged particles may swap their
positions with asymmetric rates q and 1. In this paper we assume that a finite
density of positively charged particles and only one negative particle
(which plays the role of an impurity) exist on the ring. It turns out that the
canonical partition function of this model can be calculated exactly using
Matrix Product Ansatz (MPA) formalism. In the limit of infinite system size and
infinite number of positive particles, we can also derive exact expressions for
the speed of the positive and negative particles which show a second order
phase transition at . The density profile of the positive particles
on the ring has a shock structure for and an exponential behaviour
with correlation length for . It will be shown that the
mean-field results become exact at q=3 and no phase transition occurs for q>2.Comment: 9 pages,4 EPS figures. To be appear in JP
From Sherman\u27s Army, With Love: Illinois Soldier\u27s Field Letters Address Things Back Home
Colonel Smith D. Atkins loathed General Gordon Granger and sought to persuade William Rosecrans to attach Atkins\u27s 92nd Illinois Infantry to active duty at the front. Relief came after Colonel John Wilder observed the regiment building a bridge across the Duck River, liked what he saw, and had it as...
Condensation transition in a model with attractive particles and non-local hops
We study a one dimensional nonequilibrium lattice model with competing
features of particle attraction and non-local hops. The system is similar to a
zero range process (ZRP) with attractive particles but the particles can make
both local and non-local hops. The length of the non-local hop is dependent on
the occupancy of the chosen site and its probability is given by the parameter
. Our numerical results show that the system undergoes a phase transition
from a condensate phase to a homogeneous density phase as is increased
beyond a critical value . A mean-field approximation does not predict a
phase transition and describes only the condensate phase. We provide heuristic
arguments for understanding the numerical results.Comment: 11 Pages, 6 Figures. Published in Journal of Statistical Mechanics:
Theory and Experimen
Phase transition in conservative diffusive contact processes
We determine the phase diagrams of conservative diffusive contact processes
by means of numerical simulations. These models are versions of the ordinary
diffusive single-creation, pair-creation and triplet-creation contact processes
in which the particle number is conserved. The transition between the frozen
and active states was determined by studying the system in the subcritical
regime and the nature of the transition, whether continuous or first order, was
determined by looking at the fractal dimension of the critical cluster. For the
single-creation model the transition remains continuous for any diffusion rate.
For pair- and triplet-creation models, however, the transition becomes first
order for high enough diffusion rate. Our results indicate that in the limit of
infinite diffusion rate the jump in density equals 2/3 for the pair-creation
model and 5/6 for the triplet-creation model
Boundary-induced abrupt transition in the symmetric exclusion process
We investigate the role of the boundary in the symmetric simple exclusion
process with competing nonlocal and local hopping events. With open boundaries,
the system undergoes a first order phase transition from a finite density phase
to an empty road phase as the nonlocal hopping rate increases. Using a cluster
stability analysis, we determine the location of such an abrupt nonequilibrium
phase transition, which agrees well with numerical results. Our cluster
analysis provides a physical insight into the mechanism behind this transition.
We also explain why the transition becomes discontinuous in contrast to the
case with periodic boundary conditions, in which the continuous phase
transition has been observed.Comment: 8 pages, 11 figures (12 eps files); revised as the publised versio
Nonequilibrium Phase Transitions in a Driven Sandpile Model
We construct a driven sandpile slope model and study it by numerical
simulations in one dimension. The model is specified by a threshold slope
\sigma_c\/, a parameter \alpha\/, governing the local current-slope
relation (beyond threshold), and , the mean input current of sand.
A nonequilibrium phase diagram is obtained in the \alpha\, -\, j_{\rm in}\/
plane. We find an infinity of phases, characterized by different mean slopes
and separated by continuous or first-order boundaries, some of which we obtain
analytically. Extensions to two dimensions are discussed.Comment: 11 pages, RevTeX (preprint format), 4 figures available upon requs
Spatial Particle Condensation for an Exclusion Process on a Ring
We study the stationary state of a simple exclusion process on a ring which
was recently introduced by Arndt {\it et al} [J. Phys. A {\bf 31} (1998)
L45;cond-mat/9809123]. This model exhibits spatial condensation of particles.
It has been argued that the model has a phase transition from a ``mixed phase''
to a ``disordered phase''. However, in this paper exact calculations are
presented which, we believe, show that in the framework of a grand canonical
ensemble there is no such phase transition. An analysis of the fluctuations in
the particle density strongly suggests that the same result also holds for the
canonical ensemble.Comment: 20 pages, 4 figure
A limit result for a system of particles in random environment
We consider an infinite system of particles in one dimension, each particle
performs independant Sinai's random walk in random environment. Considering an
instant , large enough, we prove a result in probability showing that the
particles are trapped in the neighborhood of well defined points of the lattice
depending on the random environment the time and the starting point of the
particles.Comment: 11 page
Hard rod gas with long-range interactions: Exact predictions for hydrodynamic properties of continuum systems from discrete models
One-dimensional hard rod gases are explicitly constructed as the limits of
discrete systems: exclusion processes involving particles of arbitrary length.
Those continuum many-body systems in general do not exhibit the same
hydrodynamic properties as the underlying discrete models. Considering as
examples a hard rod gas with additional long-range interaction and the
generalized asymmetric exclusion process for extended particles (-ASEP),
it is shown how a correspondence between continuous and discrete systems must
be established instead. This opens up a new possibility to exactly predict the
hydrodynamic behaviour of this continuum system under Eulerian scaling by
solving its discrete counterpart with analytical or numerical tools. As an
illustration, simulations of the totally asymmetric exclusion process
(-TASEP) are compared to analytical solutions of the model and applied to
the corresponding hard rod gas. The case of short-range interaction is treated
separately.Comment: 19 pages, 8 figure
Boundary-Induced Phase Transitions in Equilibrium and Non-Equilibrium Systems
Boundary conditions may change the phase diagram of non-equilibrium
statistical systems like the one-dimensional asymmetric simple exclusion
process with and without particle number conservation. Using the quantum
Hamiltonian approach, the model is mapped onto an XXZ quantum chain and solved
using the Bethe ansatz. This system is related to a two-dimensional vertex
model in thermal equilibrium. The phase transition caused by a point-like
boundary defect in the dynamics of the one-dimensional exclusion model is in
the same universality class as a continous (bulk) phase transition of the
two-dimensional vertex model caused by a line defect at its boundary.
(hep-th/yymmnnn)Comment: Latex 10pp, Geneva preprint UGVA-DPT 1993/07-82
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