Anomalous transmission and drifts in one-dimensional Levy structures

TL;DR

This paper investigates how random walkers transmit through one-dimensional Levy-structured materials with long-range correlated scatterers, revealing intrinsic asymmetries and drifts affecting transmission properties.

Contribution

It introduces a scaling framework for transmission in Levy-structured media and highlights the presence of sample-specific drifts even without bias.

Findings

Non-zero drift can occur in individual samples due to arrangement asymmetry.

Transmission scaling behavior depends on Levy spacing and correlations.

Numerical solutions confirm theoretical predictions across boundary conditions.

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 L\'evy 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.