The Excitation Spectrum for Weakly Interacting Bosons

TL;DR

This paper rigorously proves that the Bogoliubov spectrum accurately describes the low-energy excitations of a weakly interacting Bose gas in the mean-field limit, confirming longstanding theoretical predictions.

Contribution

It provides a mathematical proof that the Bogoliubov spectrum is exact for weakly interacting Bose gases in the mean-field limit.

Findings

Bogoliubov spectrum becomes exact in the mean-field limit

Linear dispersion relation for small momentum confirmed

Rigorous mathematical validation of theoretical predictions

Abstract

We investigate the low energy excitation spectrum of a Bose gas with weak, long range repulsive interactions. In particular, we prove that the Bogoliubov spectrum of elementary excitations with linear dispersion relation for small momentum becomes exact in the mean-field limit.