Localization and delocalization of ground states of Bose-Einstein condensates under disorder

TL;DR

This paper investigates how Bose-Einstein condensates localize or delocalize in disordered potentials, providing mathematical and numerical insights into the conditions influencing ground state behavior, with implications for experimental observation.

Contribution

It offers a quantitative analysis of ground state localization in Bose-Einstein condensates under disorder, linking mathematical models with numerical simulations and experimental relevance.

Findings

Exponential localization of ground states in weak interaction regimes

Delocalization occurs outside specific parameter ranges

Predictions for experimental regimes of localization

Abstract

This paper studies the localization behaviour of Bose-Einstein condensates in disorder potentials, modeled by a Gross-Pitaevskii eigenvalue problem on a bounded interval. In the regime of weak particle interaction, we are able to quantify exponential localization of the ground state, depending on statistical parameters and the strength of the potential. Numerical studies further show delocalization if we leave the identified parameter range, which is in agreement with experimental data. These mathematical and numerical findings allow the prediction of physically relevant regimes where localization of ground states may be observed experimentally.