Partially Asymmetric Exclusion Models with Quenched Disorder

We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case, the accumulated distance traveled by the particles, x, scales with the time, t, as x∼t^1/z, with a dynamical exponent z>0. Using extreme value statistics and an asymptotically exact strong disorder renormalization group method, we exactly calculate z_PW for particlewise disorder, which is argued to be related as z_SW=z_PW/2 for sitewise disorder. In the symmetric case with zero mean drift, the particle diffusion is ultraslow, logarithmic in time.