Disordered Bose Einstein Condensates with Interaction in One Dimension

TL;DR

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

Contribution

It provides a rigorous analysis of the interplay between disorder and interactions in 1D Bose gases, showing conditions for localization and delocalization of the condensate.

Findings

Bose-Einstein condensation survives strong random potentials.

Wave function extends over the entire interval at low scatterer density or strong interactions.

Wave function localizes in a fragmented subset under high scatterer density and weak interactions.

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.