# Asymmetric exclusion model with two species: Spontaneous symmetry breaking

@article{Evans1995AsymmetricEM, title={Asymmetric exclusion model with two species: Spontaneous symmetry breaking}, author={Martin R Evans and Damien Paul Foster and Claude Godr{\`e}che and David Mukamel}, journal={Journal of Statistical Physics}, year={1995}, volume={80}, pages={69-102} }

A simple two-species asymmetric exclusion model is introduced. It consists of two types of oppositely charged particles driven by an electric field and hopping on an open chain. The phase diagram of the model is calculated in the meanfield approximation and by Monte Carlo simulations. Exact solutions are given for special values of the parameters defining its dynamics. The model is found to exhibit two phases in which spontaneous symmetry breaking takes place, where the two currents of the two…

## 137 Citations

Spontaneous symmetry breaking in a non-conserving two-species driven model

- Physics
- 2004

A two-species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The…

One-dimensional asymmetric exclusion model with open boundaries

- Physics, Mathematics
- 1996

One-dimensional asymmetric exclusion model, in which the probabilities of hopping to the left and right are in general different, is studied. The boundaries are open; a particle is added at the left…

Asymmetric simple exclusion model with local inhomogeneity

- Physics
- 1998

We study a totally asymmetric simple exclusion model with open boundary conditions and a local inhomogeneity in the bulk. It consists of a one-dimensional lattice with particles hopping…

A Two-Species Exclusion Model With Open Boundaries: A use of q-deformed algebra

- Mathematics
- 2000

In this paper we study an one-dimensional two-species exclusion model with open boundaries. The model consists of two types of particles moving in opposite directions on an open lattice. Two adjacent…

Spontaneous symmetry breaking in two-channel asymmetric exclusion processes with narrow entrances

- Physics
- 2007

Multi-particle non-equilibrium dynamics in two-channel asymmetric exclusion processes with narrow entrances is investigated theoretically. Particles move on two parallel lattices in opposite…

The exact phase diagram for a class of open multispecies asymmetric exclusion processes

- PhysicsScientific Reports
- 2017

This work considers a totally asymmetric exclusion process with multiple species of particles on a one-dimensional lattice in contact with reservoirs, and derives the exact nonequilibrium phase diagram for the system in the long time limit.

Dynamical aspects of spontaneous symmetry breaking in driven flow with exclusion.

- PhysicsPhysical review. E
- 2019

A numerical study of a two-lane version of the stochastic nonequilibrium model known as the totally asymmetric simple exclusion process, which studies an adaptation of domain-wall theory to mimic the density reversal process associated with a flip.

Shocks in the asymmetry exclusion model with an impurity

- Physics
- 1996

We consider the one-dimensional asymmetric exclusion process with an impurity. This model describes particles hopping in one direction with stochastic dynamics and a hard core exclusion condition.…

## References

SHOWING 1-10 OF 28 REFERENCES

Finite-size effects for phase segregation in a two-dimensional asymmetric exclusion model with two species

- Physics
- 1994

We investigate the stationary states of a two-dimensional lattice gas model with exclusion, in the presence of an external field. The lattice is populated by equal numbers of positively and…

Phase transitions in an exactly soluble one-dimensional exclusion process

- Mathematics
- 1993

We consider an exclusion process with particles injected with rate α at the origin and removed with rate β at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop…

An exact solution of a one-dimensional asymmetric exclusion model with open boundaries

- Physics, Mathematics
- 1992

A simple asymmetric exclusion model with open boundaries is solved exactly in one dimension. The exact solution is obtained by deriving a recursion relation for the steady state: if the steady state…

Exact solution of a 1d asymmetric exclusion model using a matrix formulation

- Mathematics
- 1993

Several recent works have shown that the one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, can be…

Onset of Spatial Structures in Biased Diffusion of Two Species

- Physics
- 1992

We consider a stochastic lattice gas with equal numbers of oppositely charged particles, diffusing under the influence of a uniform external electric field and the excluded-volume condition.…

Boundary-induced phase transitions in driven diffusive systems.

- PhysicsPhysical review letters
- 1991

Steady states of driven lattice gases with open boundaries are investigated, and two types of phase transitions involving nonanalytic changes in the density profiles and the particles number fluctuation spectra are encountered upon varying the feeding rate and the particle interactions.

Exact solution of the totally asymmetric simple exclusion process: Shock profiles

- Physics
- 1993

The microscopic structure of macroscopic shocks in the one-dimensional, totally asymmetric simple exclusion process is obtained exactly from the complete solution of the stationary state of a model…

Nonequilibrium steady states of stochastic lattice gas models of fast ionic conductors

- Physics
- 1984

We investigate theoretically and via computer simulation the stationary nonequilibrium states of a stochastic lattice gas under the influence of a uniform external fieldE. The effect of the field is…

Shocks in the asymmetric exclusion process

- Mathematics
- 1988

SummaryIn this paper, we consider limit theorems for the asymmetric nearest neighbor exclusion process on the integers. The initial distribution is a product measure with asymptotic density λ at -∞…

Phase transitions induced by a defect in a growing interface model

- Materials Science
- 1993

The effect of a localized defect on the profile of a one-dimensional growing interface is considered. The (q, q') phase diagram of a restricted solid-on-solid growth model is studied within the mean…