Partially asymmetric exclusion processes with sitewise disorder

We study the stationary properties as well as the nonstationary dynamics of the one-dimensional partially asymmetric exclusion process with position-dependent random hop rates. Relating the hop rates to an energy landscape the stationary current J is determined by the largest barrier in a finite system of L sites and the corresponding waiting time tau similar to J(-1) is related to the waiting time of a single random walker, tau(rw), as tau similar to tau(1/2)(rw). The current is found to vanish as J similar to L-z/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 similar to L-1/2 connected parts of particles (holes) which are separated by islands of holes (particles) located at the subleading barriers (valleys). We also study nonstationary 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.