Anomalous diffusion in a space- and time-dependent energy landscape

Abstract

We study the influence on diffusion in one dimension of a potential energy perturbation varying as a power in space and time. We concentrate on the case of a parabolic perturbation in space decaying as $t^{-\omega }$ which shows a rich variety of scaling behaviours. When $\omega =1$, the perturbation is truly marginal and leads to anomalous (super)diffusion with a dynamical exponent varying continuously with the perturbation amplitude below some negative threshold value. For slower decay, $\omega <1$, the perturbation becomes relevant and the system is either subdiffusive for an attractive potential or displays a stretched-exponential behaviour for a repulsive one. Exact results are obtained for the mean value and the variance of the position as well as for the surviving probability.

17 pages, 5 figures. Minor corrections

References in corpus (9)

• Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk
• Inhomogeneous Systems with Unusual Critical Behaviour
• Memory-induced anomalous dynamics: emergence of diffusion, subdiffusion, and superdiffusion from a single random walk model
• Anomalous Diffusion in Aperiodic Environments
• Anomalous diffusion in disordered media and random quantum spin chains
• Comparative study of the critical behavior in one-dimensional random and aperiodic environments
• Anomalous Behavior of the Contact Process with Aging
• Transverse-field Ising spin chain with inhomogeneous disorder
• Reaction-diffusion with a time-dependent reaction rate: the single-species diffusion-annihilation process