4 research outputs found
Spurious phase in a model for traffic on a bridge
We present high-precision Monte Carlo data for the phase diagram of a
two-species driven diffusive system, reminiscent of traffic across a narrow
bridge. Earlier studies reported two phases with broken symmetry; the existence
of one of these has been the subject of some debate. We show that the disputed
phase disappears for sufficiently large systems and/or sufficiently low bulk
mobility.Comment: 8 pages, 3 figures, JPA styl
Spontaneous symmetry breaking: exact results for a biased random walk model of an exclusion process
It has been recently suggested that a totally asymmetric exclusion process
with two species on an open chain could exhibit spontaneous symmetry breaking
in some range of the parameters defining its dynamics. The symmetry breaking is
manifested by the existence of a phase in which the densities of the two
species are not equal. In order to provide a more rigorous basis to these
observations we consider the limit of the process when the rate at which
particles leave the system goes to zero. In this limit the process reduces to a
biased random walk in the positive quarter plane, with specific boundary
conditions. The stationary probability measure of the position of the walker in
the plane is shown to be concentrated around two symmetrically located points,
one on each axis, corresponding to the fact that the system is typically in one
of the two states of broken symmetry in the exclusion process. We compute the
average time for the walker to traverse the quarter plane from one axis to the
other, which corresponds to the average time separating two flips between
states of broken symmetry in the exclusion process. This time is shown to
diverge exponentially with the size of the chain.Comment: 42 page
Phase Separation and Coarsening in One-Dimensional Driven Diffusive Systems: Local Dynaimcs Leading to Long-Range Hamiltonians
A driven system of three species of particle diffusing on a ring is studied
in detail. The dynamics is local and conserves the three densities. A simple
argument suggesting that the model should phase separate and break the
translational symmetry is given. We show that for the special case where the
three densities are equal the model obeys detailed balance and the steady-state
distribution is governed by a Hamiltonian with asymmetric long-range
interactions. This provides an explicit demonstration of a simple mechanism for
breaking of ergodicity in one dimension. The steady state of finite-size
systems is studied using a generalized matrix product ansatz. The coarsening
process leading to phase separation is studied numerically and in a mean-field
model. The system exhibits slow dynamics due to trapping in metastable states
whose number is exponentially large in the system size. The typical domain size
is shown to grow logarithmically in time. Generalizations to a larger number of
species are discussed.Comment: Revtex, 29 Pages, 7 figures, uses epsf.sty, submitted to Phys. Rev.
Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
Recent work on stochastic interacting particle systems with two particle
species (or single-species systems with kinematic constraints) has demonstrated
the existence of spontaneous symmetry breaking, long-range order and phase
coexistence in nonequilibrium steady states, even if translational invariance
is not broken by defects or open boundaries. If both particle species are
conserved, the temporal behaviour is largely unexplored, but first results of
current work on the transition from the microscopic to the macroscopic scale
yield exact coupled nonlinear hydrodynamic equations and indicate the emergence
of novel types of shock waves which are collective excitations stabilized by
the flow of microscopic fluctuations. We review the basic stationary and
dynamic properties of these systems, highlighting the role of conservation laws
and kinetic constraints for the hydrodynamic behaviour, the microscopic origin
of domain wall (shock) stability and the coarsening dynamics of domains during
phase separation.Comment: 72 pages, 6 figures, 201 references (topical review for J. Phys. A:
Math. Gen.