Kinetic theory of fluctuations in conducting systems

TL;DR

This paper develops an effective field theory for electron fluctuations in conductors, linking it to quantum models and analyzing how scattering processes influence current fluctuation statistics.

Contribution

It introduces a generalized kinetic theory of fluctuations, connecting it to quantum models and exploring the impact of scattering on current cumulants.

Findings

Higher current cumulants are enhanced with short electron-electron scattering length.

The theory is equivalent to a quantum non-linear sigma model when quantum corrections are ignored.

Application to scattering effects reveals significant influence on fluctuation statistics.

Abstract

We propose an effective field theory describing the time dependent fluctuations of electrons in conducting systems, generalizing the well known kinetic theory of fluctuations. On several examples, we show its equivalence, (when quantum corrections are neglected) to a microscopic quantum mechanical non-linear $\sigma$-model theory. We apply then the theory to analyze the effects of strong electron-electron and electron-phonon scattering on the statistics of current fluctuations. We find that if the electron-electron scattering length is much shorter than the transport mean free path the higher cumulants of current are parametrically enhanced.