Statistics of Rare Events in Disordered Conductors

TL;DR

This paper investigates the rare event statistics in disordered conductors using an optimal fluctuation method, revealing new asymptotics that differ from previous models, especially in low-dimensional systems.

Contribution

It introduces an optimal fluctuation approach for analyzing rare events in disordered conductors, outperforming nonlinear sigma-models in handling large fluctuations.

Findings

New asymptotic distribution functions for 2D and 3D conductors.

Significant differences from previous results in certain cases.

Method effectively captures large amplitude fluctuations.

Abstract

Asymptotic behavior of distribution functions of local quantities in disordered conductors is studied in the weak disorder limit by means of an optimal fluctuation method. It is argued that this method is more appropriate for the study of seldom occurring events than the approaches based on nonlinear $\sigma$-models because it is capable of correctly handling fluctuations of the random potential with large amplitude as well as the short-scale structure of the corresponding solutions of the Schr\"{o}dinger equation. For two- and three-dimensional conductors new asymptotics of the distribution functions are obtained which in some cases differ significantly from previously established results.