Coherent wave transmission in quasi-one-dimensional systems with L\'evy disorder

TL;DR

This paper investigates how Levy-distributed disorder affects wave transmission in quasi-one-dimensional systems, revealing large transmission fluctuations and anomalous localization, with theoretical and numerical analysis comparing to standard Anderson localization.

Contribution

It provides a comprehensive analysis of transmission fluctuations in Levy-disordered systems, highlighting differences from Anderson localization and confirming results with numerical simulations.

Findings

Levy disorder causes large transmission fluctuations.

Anomalous localization differs from standard Anderson localization.

Theoretical predictions are validated by numerical simulations.

Abstract

We study the random fluctuations of the transmission in disordered quasi-one-dimensional systems such as disordered waveguides and/or quantum wires whose random configurations of disorder are characterized by density distributions with a long tail known as L\'evy distributions. The presence of L\'evy disorder leads to large fluctuations of the transmission and anomalous localization, in relation to the standard exponential localization (Anderson localization). We calculate the complete distribution of the transmission fluctuations for different number of transmission channels in the presence and absence of time-reversal symmetry. Significant differences in the transmission statistics between disordered systems with Anderson and anomalous localizations are revealed. The theoretical predictions are independently confirmed by tight binding numerical simulations.