Disordered Totally Asymmetric Simple Exclusion Process: Exact Results

TL;DR

This paper derives exact analytical expressions for the steady-state weights and current in a disordered totally asymmetric simple exclusion process, revealing a novel symmetry related to particle-hole transformation and jump direction reversal.

Contribution

It provides the first exact solutions for the disordered TASEP's steady states and uncovers a symmetry linking current invariance under jump direction reversal.

Findings

Exact expressions for steady-state weights and current

Proof of invariance of current under jump reversal

Identification of a particle-hole symmetry in disordered TASEP

Abstract

We study the effect of quenched spatial disorder on the current-carrying steady states of the totally asymmetric simple exclusion process with spatially disordered jump rates. The exact analytical expressions for the steady-state weights, and the current are found for this model in one dimension. We demonstrate how these solutions can be exploited to study analytically the exact symmetries of the system. In particular, we prove that the magnitude of the steady-state current is left invariant when the direction of all the allowed particle jumps are reversed. Or equivalently, we prove that for any given filling and disorder configuration, particle-hole transformation is an exact symmetry that leaves the steady-state current invariant. This non-trivial symmetry was recently demonstrated in numerical simulations by Tripathy & Burma (preprint cond-mat/9711302).