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 identical with <k>/R of the bath jump rate R and the average hopping rate <k>. When kappaN approximately 1, 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, approximately N1+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.
Barsegov
Valeri
V
Department of Chemistry, University of Rochester, Rochester, New York 14627-0216, USA.
Shapir
Yonathan
Y
Mukamel
Shaul
S