Long--time relaxation of current in a 2D weakly disordered conductor

TL;DR

This paper investigates the long-time relaxation behavior of conductance in 2D disordered conductors using a supermatrix sigma-model approach, confirming results with renormalization group analysis.

Contribution

It applies a saddle-point approximation to the sigma-model to analyze conductance relaxation, aligning with prior renormalization group findings.

Findings

Asymptotic behavior matches renormalization group results

Method confirms long-time conductance relaxation dynamics

Supermatrix sigma-model effectively describes 2D disordered conductors

Abstract

The long-time relaxation of the average conductance in a 2D mesoscopic sample is studied within the method recently suggested by Muzykantskii and Khmelnitskii and based on a saddle-point approximation to the supermatrix $\sigma$--model. The obtained far asymptotics is in perfect agreement with the result of renormalization group treatment by Altshuler, Kravtsov and Lerner.