Disordered totally asymmetric simple exclusion process: Exact results

Abstract

We study the effect of quenched spatial disorder on the current-carrying steady states of a totally asymmetric simple exclusion process with spatially disordered jump rates. Expressions for the steady state weights and the current are derived for this model in one dimension. These solutions are exploited to study analytically the exact symmetries of the system. In particular, we confirm the recent numerical observation of Tripathy and Barma [Phys. Rev. E 58, 1911 (1998)] that the magnitude of the steady state current is left invariant when the direction of all the allowed particle jumps are reversed.