Anomalous transmission and drifts in one-dimensional Levy structures

Abstract

We study the transmission of random walkers through a finite-size inhomogeneous material with a quenched, long-range correlated distribution of scatterers. We focus on a finite one-dimensional structure where walkers undergo random collisions with a subset of sites distributed on deterministic (Cantor-like) or random positions, with Lévy spaced distances. Using scaling arguments, we consider stationary and time-dependent transmission and we provide predictions on the scaling behaviour of particle current as a function of the sample size. We show that, even in absence of bias, for each single realization a non-zero drift can be present, due to the intrinsic asymmetry of each specific arrangement of the scattering sites. For finite systems, this average drift is particularly important for characterizing the transmission properties of individual samples. The predictions are tested against the numerical solution of the associated master equation. A comparison of different boundary conditions is given.

arXiv commentSubmitted to Chaos, Solitons and Fractals

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• Strong anomalous diffusion in two-state process with Lévy walk and Brownian motion
• Strong anomalous diffusion of the phase of a chaotic pendulum
• A Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems