title: Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder.
abstract: 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.
authors.affiliation: Laboratoire de Physique Théorique de la Matière Condensée, UMR CNRS 7600, Université Pierre et Marie Curie, Paris 6, -4 Place Jussieu, 75252 Paris, France. oshanin@lptmc.jussieu.fr
authors.forename: Gleb
authors.initials: G
authors.lastname: Oshanin
authors.forename: Alberto
authors.initials: A
authors.lastname: Rosso
authors.forename: Grégory
authors.initials: G
authors.lastname: Schehr