Excitation spectrum of interacting bosons in the mean-field infinite-volume limit

TL;DR

This paper rigorously analyzes the excitation spectrum of a homogeneous Bose gas in the mean-field infinite-volume limit, confirming the Bogoliubov approximation's predictions for large systems at zero temperature.

Contribution

It extends previous results to large volumes, providing a rigorous proof that the excitation spectrum matches the Bogoliubov approximation in the mean-field limit.

Findings

Excitation spectrum aligns with Bogoliubov predictions

Results valid for large volumes and zero temperature

Extends prior work to infinite-volume limit

Abstract

We consider homogeneous Bose gas in a large cubic box with periodic boundary conditions, at zero temperature. We analyze its excitation spectrum in a certain kind of a mean field infinite volume limit. We prove that under appropriate conditions the excitation spectrum has the form predicted by the Bogoliubov approximation. Our result can be viewed as an extension of the result of R. Seiringer (arXiv:1008.5349 [math-ph]) to large volumes.