One-dimensional transport with dynamic disorder

Abstract

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 $\kappa \equiv 〈k〉/R$ of the bath jump rate R and the average hopping rate $〈k〉.$ When $\kappa N\sim 1,$ the quenching time distribution has long power-law tails even when the waiting times are exponentially distributed. These disappear for $\kappa N\ll 1$ 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, $\sim N^{1+\gamma },$ 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.