Bogoliubov excitation spectrum for Bose-Einstein condensates

TL;DR

This paper rigorously confirms Bogoliubov's predictions for the ground state energy and low-energy excitations of weakly interacting Bose gases in a box, within the Gross-Pitaevskii limit.

Contribution

It provides a mathematical proof validating Bogoliubov's theory for Bose-Einstein condensates in a confined box under weak interactions.

Findings

Validation of Bogoliubov's prediction for ground state energy

Confirmation of low-energy excitation spectrum accuracy

Results applicable in the Gross-Pitaevskii limit

Abstract

We consider interacting Bose gases trapped in a box $\Lambda = [0;1]^3$ in the Gross-Pitaevskii limit. Assuming the potential to be weak enough, we establish the validity of Bogoliubov's prediction for the ground state energy and the low-energy excitation spectrum. These notes are based on \cite{BBCS3}, a joint work with C. Boccato, C. Brennecke and S. Cenatiempo.