Bogoliubov Theory in the Gross-Pitaevskii Limit

TL;DR

This paper rigorously analyzes the ground state energy and low-energy excitations of Bose gases in the Gross-Pitaevskii limit, confirming Bogoliubov's theoretical predictions with precise asymptotics.

Contribution

It provides a rigorous derivation of the ground state energy and excitation spectrum for Bose gases in the Gross-Pitaevskii regime, validating Bogoliubov's theory.

Findings

Ground state energy matches Bogoliubov's predictions

Low-energy excitation spectrum is accurately characterized

Errors vanish as particle number increases

Abstract

We consider Bose gases consisting of $N$ particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of the order $N^{-1}$(Gross-Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing as $N \to \infty$. Our results confirm Bogoliubov's predictions.