Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder

Gleb Oshanin 1, Alberto Rosso 2, Gregory Schehr 2

Physical Review Letters 110 (2013) 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 counter-intuitive behavior is explained via an analysis of representative realizations of disorder.

  • 1 : Laboratoire de Physique Théorique de la Matière Condensée (LPTMC)
    CNRS : UMR7600 – Université Pierre et Marie Curie (UPMC) - Paris VI
  • 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
    CNRS : UMR8626 – Université Paris XI - Paris Sud