Partially Asymmetric Exclusion Processes with Sitewise Disorder

We study the stationary properties as well as the non-stationary dynamics of the one-dimensional partially asymmetric exclusion process with position dependent random hop rates. In a finite system of $L$ sites the stationary current, $J$, is determined by the largest barrier and the corresponding waiting time, $\tau \sim J^{-1}$, is related to the waiting time of a single random walker, ${\tau }_{rw}$, as $\tau \sim {\tau }_{rw}^{1\mathrm{/}2}$. The current is found to vanish as: $J\sim L^{-z\mathrm{/}2}$, where $z$ is the dynamical exponent of the biased single particle Sinai walk. Typical stationary states are phase separated: At the largest barrier almost all particles queue at one side and almost all holes are at the other side. The high-density (low-density) region, is divided into $\sim L^{1\mathrm{/}2}$ connected parts of particles (holes) which are separated by islands of holes (particles) located at the subleading barriers (valleys). We also study non-stationary processes of the system, like coarsening and invasion. Finally we discuss some related models, where particles of larger size or multiple occupation of lattice sites is considered.