Semiclassical kinetic equations for composite bosons

TL;DR

This paper develops semiclassical Boltzmann equations for excitons, accounting for their composite nature, and explores how this affects thermalization, addressing particle number conservation issues with angular momentum algebra.

Contribution

It introduces a novel approach to derive kinetic equations for composite bosons, incorporating their non-ideal statistics and resolving particle number conservation problems.

Findings

Composite excitons influence thermalization dynamics.

Angular momentum algebra helps conserve particle number.

Derived kinetic equations describe exciton density evolution.

Abstract

We derive semiclassical Boltzmann equations describing thermalization of an ensemble of excitons due to exciton-phonon interactions taking into account the fact that excitons are not ideal bosons but composite particles consisting of electrons and holes. We demonstrate that with a standard definition of excitonic creation and annihilation operators, one faces a problem of the total particle number nonconservation and propose its possible solution based on the introduction of operators with angular momentum algebra. We then derive a set of kinetic equations describing the evolution of the excitonic density in the reciprocal space and analyze how the composite statistics of the excitons affects the thermalization processes in the system.