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 pro cess with two species on an open chain could exhibit spontaneous symme try breaking in some range of the parameters defining its dynamics. Th e 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 th e process when the rate at which particles leave the system goes to ze ro. In this limit the process reduces to a biased random walk in the p ositive quarter plane, with specific boundary conditions. The stationa ry probability measure of the position of the walker in the plane is s hown to be concentrated around two symmetrically located points, one o n 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 sep arating two flips between states of broken symmetry in the exclusion p rocess. This time is shown to diverge exponentially with the size of t he chain.