The Boltzmann--Langevin approach: A simple quantum-mechanical derivation

TL;DR

This paper provides a straightforward quantum-mechanical derivation of the correlation functions in the Boltzmann--Langevin equation, focusing on electron-phonon scattering, and demonstrates that weak scattering results in Poisson-distributed fluxes.

Contribution

It offers a novel, simplified quantum derivation of Langevin source correlations, clarifying assumptions about scattering processes in semiclassical transport.

Findings

Correlation functions derived quantum-mechanically

Poisson distribution of scattering fluxes established

Weak scattering assumption validated

Abstract

We present a simple quantum-mechanical derivation of correlation function of Langevin sources in the semiclassical Boltzmann--Langevin equation. The specific case of electron--phonon scattering is considered. It is shown that the assumption of weak scattering leads to the Poisson nature of the scattering fluxes.