Microscopic scattering theory for interacting bosons in weak random potentials

TL;DR

This paper develops a microscopic scattering theory for interacting bosons in weak disordered potentials, revealing how inelastic collisions induce thermalization and affect coherent backscattering in quantum transport.

Contribution

It introduces a diagrammatic N-body scattering framework that accounts for elastic and inelastic collisions, extending mean-field models to include thermalization and localization effects.

Findings

Inelastic collisions cause energy redistribution and thermalization.

Weak localization effects are incorporated, showing enhanced backscattering.

The theory reduces to the Gross-Pitaevskii equation when only elastic collisions are considered.

Abstract

We develop a diagrammatic scattering theory for interacting bosons in a three-dimensional, weakly disordered potential. Based on a microscopic N-body scattering theory, we identify the relevant diagrams including elastic and inelastic collision processes that are sufficient to describe diffusive quantum transport. By taking advantage of the statistical properties of the weak disorder potential, we demonstrate how the N-body dynamics can be reduced to a nonlinear integral equation of Boltzmann type for the single-particle diffusive flux. Our theory reduces to the Gross-Pitaevskii mean field description in the limit where only elastic collisions are taken into account. However, even at weak interaction strength, inelastic collisions lead to energy redistribution between the bosons - initially prepared all at the same single-particle energy - and thereby induce thermalization of the single-particle current. In addition, we include also weak localization effects and determine the coherent corrections to the incoherent transport in terms of the coherent backscattering signal. We find that inelastic collisions lead to an enhancement of the backscattered cone in a narrow spectral window for increasing interaction strength.