  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).
