The excitation spectrum of two dimensional Bose gases in the Gross-Pitaevskii regime

TL;DR

This paper rigorously confirms Bogoliubov theory's predictions for the ground state energy and low-energy excitations of a large two-dimensional Bose gas with exponentially small scattering length in the Gross-Pitaevskii regime.

Contribution

It provides a mathematical proof validating Bogoliubov theory for the excitation spectrum of 2D Bose gases in the Gross-Pitaevskii regime.

Findings

Ground state energy matches Bogoliubov predictions

Low-energy excitation spectrum is accurately described

Errors vanish as particle number N increases

Abstract

We consider a system of $N$ bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two-body potential, with a scattering length that is exponentially small in $N$ (Gross-Pitaevskii regime). In this setting, we establish the validity of the predictions of Bogoliubov theory, determining the ground state energy of the Hamilton operator and its low-energy excitation spectrum, up to errors that vanish in the limit $N \to \infty$.