One-dimensional transport with dynamic disorder

We study the mean quenching time distribution and its moments in a one-dimensional N-site donor-bridge-acceptor system where all sites are coupled to a two-state jump bath for arbitrary disorder and an arbitrary ratio kappa=<k>/R of the bath jump rate R and the average hopping rate <k>. When kappaNsimilar to1, the quenching time distribution has long power-law tails even when the waiting times are exponentially distributed. These disappear for kappaN<<1 where the hopping rate self-averages on the bath relaxation time scale. In the absence of disorder or for small kappa, the mean quenching time scales linearly with N. Otherwise, we observe a power law, similar toN(1+gamma), with a crossover to linear scaling (gamma=0) for large N. Distributions of particle position, its second moment, velocity and diffusion coefficient are computed in the infinite N limit. For times longer than R-1, the dynamic disorder self-averages and the average position, velocity, and diffusion coefficient scale linearly in time.