Abstract
We study the dynamics of a Brownian particle in a strongly correlated quenched random potential defined as a periodically–extended (with period L) finite trajectory of a fractional Brownian motion with arbitrary Hurst exponent . While the periodicity ensures that the ultimate long–time behavior is diffusive, the generalized Sinai potential considered here leads to a strong logarithmic confinement of particle trajectories at intermediate times. These two competing trends lead to dynamical frustration and result in a rich statistical behavior of the diffusion coefficient DL: although one has the typical value , we show via an exact analytical approach that the positive moments () scale like , and the negative ones as , and being numerical constants and β the inverse temperature. These results demonstrate that DL is strongly non-self-averaging. We further show that the probability distribution of DL has a log–normal left tail and a highly singular, one–sided log–stable right tail reminiscent of a Lifshitz singularity.
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