The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime

TL;DR

This paper reviews the proof that Bogoliubov's theory accurately predicts the ground state energy and low-energy excitation spectrum of an interacting Bose gas in the Gross-Pitaevskii regime.

Contribution

It provides a rigorous validation of Bogoliubov's predictions for the excitation spectrum in the Gross-Pitaevskii limit.

Findings

Confirmation of Bogoliubov's prediction for ground state energy

Validation of low-energy excitation spectrum accuracy

Rigorous mathematical proof in the Gross-Pitaevskii regime

Abstract

We consider a gas of interacting bosons trapped in a box of side length one in the Gross-Pitaevskii limit. We review the proof of the validity of Bogoliubov's prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.