# Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime

## TL;DR

This paper proves that in the Gross-Pitaevskii regime, bosonic systems exhibit complete Bose-Einstein condensation with optimal bounds, extending previous results by removing interaction potential restrictions.

## Contribution

It establishes the optimal rate of Bose-Einstein condensation in the Gross-Pitaevskii regime without assuming small interaction potentials.

## Key findings

- Complete Bose-Einstein condensation in low-energy states
- Optimal bounds on orthogonal excitations
- Extension of previous results to larger interaction potentials

## Abstract

We consider systems of bosons trapped in a box, in the Gross-Pitaevskii regime. We show that low-energy states exhibit complete Bose-Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in \cite{BBCS1}, removing the assumption of small interaction potential.