Disordered Bose Einstein Condensates with Interaction

TL;DR

This paper investigates how random scatterers affect the ground state of one-dimensional interacting bosons, showing that Bose-Einstein condensation persists despite strong disorder, with the wave function's nature depending on the interplay of randomness and interaction strength.

Contribution

It provides a rigorous analysis of the survival and character of Bose-Einstein condensation in disordered one-dimensional Bose gases within the Lieb-Liniger model.

Findings

Condensation survives strong random potentials.

Wave function extends or localizes depending on scatterer density and interaction strength.

Disorder induces wave function fragmentation under certain conditions.

Abstract

We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the interval.