On Bose-Einstein condensates in disordered media

TL;DR

This paper studies how interacting bosons in disordered potentials exhibit slow transport, showing that fluctuations around a localized condensate propagate slowly due to disorder, with a new analysis technique for many-body systems.

Contribution

It introduces a novel interaction picture analysis to prove slow transport in disordered many-body bosonic systems with Anderson localization.

Findings

Fluctuations propagate with small velocity due to disorder

Provides an example of slow transport in any spatial dimension

Uses a new interaction picture analysis relative to Anderson localization

Abstract

We consider the quantum dynamics of interacting bosons in the mean-field regime when they are subjected to a disordered potential, which is either random or quasi-periodic. Starting from a spatially localized Bose-Einstein condensate, we prove that fluctuations around the condensate propagate with a small velocity due to the disorder. This provides an example of a disordered many-body system with provably slow transport behavior in any spatial dimension. The main technical novelty is an interaction picture analysis relative to the Anderson-localized one-body dynamics.