Bogoliubov Theory for Trapped Bosons in the Gross-Pitaevskii Regime

TL;DR

This paper rigorously analyzes the ground state energy and low-energy excitations of large trapped bosonic systems in the Gross-Pitaevskii regime, providing precise asymptotic results as the number of particles grows.

Contribution

It establishes the leading order and excitation spectrum for trapped bosons in the Gross-Pitaevskii regime with rigorous error bounds.

Findings

Ground state energy asymptotics derived

Low-energy excitation spectrum characterized

Errors vanish as particle number increases

Abstract

We consider systems of $N$ bosons in $\mathbb{R}^3$, trapped by an external potential. The interaction is repulsive and has a 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 that vanish in the limit $N\to \infty$.