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

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.