Electron random walk in ideal phonon gas. Exact dressed electron density matrix evolution equations

TL;DR

This paper introduces an exact set of evolution equations for a quantum electron interacting with an ideal phonon gas, providing a new framework to analyze electron dynamics and fluctuations in semiconductors.

Contribution

It presents a novel approach to derive exact evolution equations for the electron density matrix and correlations in a phonon environment, extending beyond previous approximate methods.

Findings

Derived exact evolution equations for electron density matrix and correlations.

Potential application to explain 1/f-type fluctuations in electron mobility.

Analyzed the case of electron in static disorder.

Abstract

An original approach is suggested to analysis of full quantum Liouville equation for single electron (quantum particle) interacting with ideal phonon gas (harmonic boson thermostat). It is shown that under the thermodynamic limit this equation can be exactly reduced to a system of evolution equations connecting density matrix of the electron and its simplest irreducible correlations with amplitudes of one, two, three and more phonon modes. Possible application of these new equations to explanation of the electron mobility 1/f-type fluctuations in semiconductors and other media is discussed. The special case of electron in static disorder is also considered.