Anomalous Fluctuations of Currents in Sinai-Type Random Chains with Strongly Correlated Disorder

作者：Oshanin Gleb^*; Rosso Alberto; Schehr Gregory

来源：Physical Review Letters, 2013, 110(10): 100602.

DOI：10.1103/PhysRevLett.110.100602

We study properties of a random walk in a generalized Sinai model, in which a quenched random potential is a trajectory of a fractional Brownian motion with arbitrary Hurst parameter H, 0 < H < 1, so that the random force field displays strong spatial correlations. In this case, the disorder-average mean-square displacement grows in proportion to log(2/H)(n), n being time. We prove that moments of arbitrary order k of the steady-state current J(L) through a finite segment of length L of such a chain decay as L-(1-H), independently of k, which suggests that despite a logarithmic confinement the average current is much higher than its Fickian counterpart in homogeneous systems. Our results reveal a paradoxical behavior such that, for fixed n and L, the mean- square displacement decreases when one varies H from 0 to 1, while the average current increases. This counterintuitive behavior is explained via an analysis of representative realizations of disorder. DOI: 10.1103/PhysRevLett.110.100602

• 出版日期2013-3-8