Kinetic localization via Poincar\'e-type inequalities and applications to the condensation of Bose gases

TL;DR

This paper introduces a simplified localization technique using Poincaré-type inequalities to derive Bose--Einstein condensation in dilute Bose gases beyond traditional scaling regimes.

Contribution

It presents a novel localization method that extends the derivation of Bose--Einstein condensation beyond the Gross--Pitaevskii regime.

Findings

New localization method based on Poincaré inequalities

Derivation of Bose--Einstein condensation beyond standard regimes

Applicable to dilute Bose gases

Abstract

We propose a simplified localization method for Bose gases, based on a Poincare-type inequality, which leads to a new derivation of Bose--Einstein condensation for dilute Bose gases beyond the Gross--Pitaevskii scaling regime.