471 research outputs found
Exact solution of an exclusion process with three classes of particles and vacancies
We present an exact solution for an asymmetric exclusion process on a ring
with three classes of particles and vacancies. Using a matrix product Ansatz,
we find explicit expressions for the weights of the configurations in the
stationary state. The solution involves tensor products of quadratic algebras.Comment: 18 pages, no figures, LaTe
Criterion for phase separation in one-dimensional driven systems
A general criterion for the existence of phase separation in driven
one-dimensional systems is proposed. It is suggested that phase separation is
related to the size dependence of the steady-state currents of domains in the
system. A quantitative criterion for the existence of phase separation is
conjectured using a correspondence made between driven diffusive models and
zero-range processes. Several driven diffusive models are discussed in light of
the conjecture
Family of Commuting Operators for the Totally Asymmetric Exclusion Process
The algebraic structure underlying the totally asymmetric exclusion process
is studied by using the Bethe Ansatz technique. From the properties of the
algebra generated by the local jump operators, we explicitly construct the
hierarchy of operators (called generalized hamiltonians) that commute with the
Markov operator. The transfer matrix, which is the generating function of these
operators, is shown to represent a discrete Markov process with long-range
jumps. We give a general combinatorial formula for the connected hamiltonians
obtained by taking the logarithm of the transfer matrix. This formula is proved
using a symbolic calculation program for the first ten connected operators.
Keywords: ASEP, Algebraic Bethe Ansatz.
Pacs numbers: 02.30.Ik, 02.50.-r, 75.10.Pq.Comment: 26 pages, 1 figure; v2: published version with minor changes, revised
title, 4 refs adde
Matrix product approach for the asymmetric random average process
We consider the asymmetric random average process which is a one-dimensional
stochastic lattice model with nearest neighbour interaction but continuous and
unbounded state variables. First, the explicit functional representations,
so-called beta densities, of all local interactions leading to steady states of
product measure form are rigorously derived. This also completes an outstanding
proof given in a previous publication. Then, we present an alternative solution
for the processes with factorized stationary states by using a matrix product
ansatz. Due to continuous state variables we obtain a matrix algebra in form of
a functional equation which can be solved exactly.Comment: 17 pages, 1 figur
Calibration of the Particle Density in Cellular-Automaton Models for Traffic Flow
We introduce density dependence of the cell size in cellular-automaton models
for traffic flow, which allows a more precise correspondence between real-world
phenomena and what observed in simulation. Also, we give an explicit
calibration of the particle density particularly for the asymmetric simple
exclusion process with some update rules. We thus find that the present method
is valid in that it reproduces a realistic flow-density diagram.Comment: 2 pages, 2 figure
Exact stationary state for a deterministic high speed traffic model with open boundaries
An exact solution for a high speed deterministic traffic model with open
boundaries and synchronous update rule is presented. Because of the strong
correlations in the model, the qualitative structure of the stationary state
can be described for general values of the maximum speed. It is shown in the
case of that a detailed analysis of this structure leads to an
exact solution. Explicit expressions for the stationary state probabilities are
given in terms of products of matrices. From this solution an
exact expression for the correlation length is derived.Comment: 20 pages, LaTeX, typos corrected and references adde
A multi-species asymmetric simple exclusion process and its relation to traffic flow
Using the matrix product formalism we formulate a natural p-species
generalization of the asymmetric simple exclusion process. In this model
particles hop with their own specific rate and fast particles can overtake slow
ones with a rate equal to their relative speed. We obtain the algebraic
structure and study the properties of the representations in detail. The
uncorrelated steady state for the open system is obtained and in the ( limit, the dependence of its characteristics on the distribution of
velocities is determined. It is shown that when the total arrival rate of
particles exceeds a certain value, the density of the slowest particles rises
abroptly.Comment: some typos corrected, references adde
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