Radiative Transport in a Periodic Structure

TL;DR

This paper derives radiative transport equations for Schrödinger solutions in periodic structures with random inhomogeneities, linking Bloch spectrum and random fluctuations to transport behavior.

Contribution

It introduces a systematic derivation of radiative transport equations using Wigner transform and Bloch wave expansion for periodic Schrödinger equations with randomness.

Findings

Transport equations depend on Bloch spectrum and random fluctuations

Streaming is determined by Bloch spectrum

Scattering is influenced by random inhomogeneities

Abstract

We derive radiative transport equations for solutions of a Schr\"odinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the radiative transport equations is determined entirely by the Bloch spectrum, while the scattering part by the random fluctuations.