On Bose-Einstein condensates in the Thomas-Fermi regime

TL;DR

This paper rigorously analyzes Bose-Einstein condensates in the Thomas-Fermi regime, demonstrating ground state condensation and its persistence over time under specific interaction scaling conditions.

Contribution

It proves complete Bose-Einstein condensation at the ground state level and shows its preservation during evolution for certain interaction parameters.

Findings

Complete Bose-Einstein condensation at ground state

Condensation preserved over time for β in (0,1/6)

Rigorous mathematical proof of condensation properties

Abstract

We study a system of $ N $ trapped bosons in the Thomas-Fermi regime with an interacting pair potential of the form $ g_N N^{3\beta-1} V(N^\beta x) $, for some $ \beta\in(0,1/3) $ and $ g_N $ diverging as $ N \to \infty $. We prove that there is complete Bose-Einstein condensation at the level of the ground state and, furthermore, that, if $ \beta\in (0,1/6) $, condensation is preserved by the time evolution.