Exponential Control of Excitations for Trapped BEC in the Gross-Pitaevskii Regime

TL;DR

This paper establishes exponential bounds on the number of particles outside the condensate in trapped Bose gases within the Gross-Pitaevskii regime, extending previous translation-invariant results to more general trapping scenarios.

Contribution

It provides the first exponential control of excitations in trapped Bose gases in the Gross-Pitaevskii regime, broadening the understanding of Bose-Einstein condensation in realistic trapping potentials.

Findings

Exponential control of orthogonal particles established

Generalization from translation-invariant to trapped systems

Improved understanding of condensate stability

Abstract

We consider trapped Bose gases in three dimensions in the Gross-Pitaevskii regime whose low energy states are well known to exhibit Bose-Einstein condensation. That is, the majority of the particles occupies the same condensate state. We prove exponential control of the number of particles orthogonal to the condensate state, generalizing recent results for translation invariant systems.