298 research outputs found
Multi-Species Asymmetric Exclusion Process in Ordered Sequential Update
A multi-species generalization of the asymmetric simple exclusion process
(ASEP) is studied in ordered sequential and sub-lattice parallel updating
schemes. In this model particles hop with their own specific probabilities to
their rightmost empty site and fast particles overtake slow ones with a
definite probability. Using Matrix Product Ansatz (MPA), we obtain the relevant
algebra, and study the uncorrelated stationary state of the model both for an
open system and on a ring. A complete comparison between the physical results
in these updates and those of random sequential introduced in [20,21] is made.Comment: Latex file 36 pages with 10 EPS figure
Finite-dimensional representation of the quadratic algebra of a generalized coagulation-decoagulation model
The steady-state of a generalized coagulation-decoagulation model on a
one-dimensional lattice with reflecting boundaries is studied using a
matrix-product approach. It is shown that the quadratic algebra of the model
has a four-dimensional representation provided that some constraints on the
microscopic reaction rates are fulfilled. The dynamics of a product shock
measure with two shock fronts, generated by the Hamiltonian of this model, is
also studied. It turns out that the shock fronts move on the lattice as two
simple random walkers which repel each other provided that the same constraints
on the microscopic reaction rates are satisfied.Comment: Minor revision
Repelling Random Walkers in a Diffusion-Coalescence System
We have shown that the steady state probability distribution function of a
diffusion-coalescence system on a one-dimensional lattice of length L with
reflecting boundaries can be written in terms of a superposition of double
shock structures which perform biased random walks on the lattice while
repelling each other. The shocks can enter into the system and leave it from
the boundaries. Depending on the microscopic reaction rates, the system is
known to have two different phases. We have found that the mean distance
between the shock positions is of order L in one phase while it is of order 1
in the other phase.Comment: 5 pages, 1 EPS figure, Accepted for publication in PRE (2008
Exact Solution of a Reaction-Diffusion Model with Particle Number Conservation
We analytically investigate a 1d branching-coalescing model with reflecting
boundaries in a canonical ensemble where the total number of particles on the
chain is conserved. Exact analytical calculations show that the model has two
different phases which are separated by a second-order phase transition. The
thermodynamic behavior of the canonical partition function of the model has
been calculated exactly in each phase. Density profiles of particles have also
been obtained explicitly. It is shown that the exponential part of the density
profiles decay on three different length scales which depend on total density
of particles.Comment: 7 pages, REVTEX4, Contents updated and new references added, to
appear in Physical Review
Discontinuous Phase Transition in an Exactly Solvable One-Dimensional Creation-Annihilation System
An exactly solvable reaction-diffusion model consisting of first-class
particles in the presence of a single second-class particle is introduced on a
one-dimensional lattice with periodic boundary condition. The number of
first-class particles can be changed due to creation and annihilation
reactions. It is shown that the system undergoes a discontinuous phase
transition in contrast to the case where the density of the second-class
particles is finite and the phase transition is continuous.Comment: Revised, 8 pages, 1 EPS figure. Accepted for publication in Journal
of Statistical Mechanics: theory and experimen
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
Connection between matrix-product states and superposition of Bernoulli shock measures
We consider a generalized coagulation-decoagulation system on a
one-dimensional discrete lattice with reflecting boundaries. It is known that a
Bernoulli shock measure with two shock fronts might have a simple random-walk
dynamics, provided that some constraints on the microscopic reaction rates of
this system are fulfilled. Under these constraints the steady-state of the
system can be written as a linear superposition of such shock measures. We show
that the coefficients of this expansion can be calculated using the
finite-dimensional representation of the quadratic algebra of the system
obtained from a matrix-product approach.Comment: 5 page
The quantum double well anharmonic oscillator in an external field
The aim of this paper is twofold. First of all, we study the behaviour of the
lowest eigenvalues of the quantum anharmonic oscillator under influence of an
external field. We try to understand this behaviour using perturbation theory
and compare the results with numerical calculations. This brings us to the
second aim of selecting the best method to carry out the numerical calculations
accurately.Comment: 9 pages, 6 figure
The Study of Shocks in Three-States Driven-Diffusive Systems: A Matrix Product Approach
We study the shock structures in three-states one-dimensional
driven-diffusive systems with nearest neighbors interactions using a matrix
product formalism. We consider the cases in which the stationary probability
distribution function of the system can be written in terms of superposition of
product shock measures. We show that only three families of three-states
systems have this property. In each case the shock performs a random walk
provided that some constraints are fulfilled. We calculate the diffusion
coefficient and drift velocity of shock for each family.Comment: 15 pages, Accepted for publication in Journal of Statistical
Mechanics: Theory and Experiment (JSTAT
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