Field Theory for the Global Density of States Distribution Function in Disordered Conductors

TL;DR

This paper introduces a novel field-theoretical approach to analyze the full distribution of the density of states in disordered conductors, enabling detailed study of fluctuation statistics.

Contribution

It develops a new functional integration method over bi-local functions, leading to an analog of the nonlinear sigma-model for the density of states distribution.

Findings

Derived the long-tail asymptotics of P(ν)

Established a formalism for complete fluctuation statistics

Introduced a supermatrix field Q(r; r_1, r_2)

Abstract

A field-theoretical representation is suggested for the electron global density of states distribution function P(\nu) in extended disordered conductors. This opens a way to study the complete statistics of fluctuations. The approach is based on a functional integration over bi-local functions \Psi(r_1, r_2) instead of the integration over local functions in the usual functional representation for moments of physical quantities. The formalism allows one to perform the disorder averaging and to derive an analog of the usual nonlinear sigma-model - a "slow" functional of a supermatrix field Q(r; r_1, r_2) \sim \Psi(r, r_1) \circ \bar{\Psi}(r_2, r). As an application of the formalism, the long-tail asymptotics of P(\nu) is derived.