Joint DIMACS, Math/physics Seminar


The Asymmetric Exclusion Process on a Lattice


Laboratoire de Physique Statistique


Hill Center, Room 705,
Busch Campus, Rutgers University.


1:30 PM
Thursday, November 7, 1996

A series of exact results have been obtained recently for the one dimensional asymmetric exclusion model, a model of particles which hop to their right at random times, on a one dimensional lattice, provided that the site they jump to is empty. The steady state properties can be calculated exactly using a matrix formulation. It consists in writing the steady state weights of a system of $N$ sites as the matrix element of a product of $N$ matrices: in this product, each matrix can take two possible forms $D$ or $E$ depending on whether the corresponding site is occupied or empty.

Several extensions of the model have been solved exactly using this matrix method, allowing the calculation of the diffusion constant of a tagged particle, of the profile of a shock and of the steady state properties of systems with two species of particles.

Document last modified on September 23, 1996