Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime

TL;DR

This paper analyzes the excitation spectrum of Bose gases in regimes between the Gross-Pitaevskii and thermodynamic limits, providing precise energy and spectrum estimates for large particle numbers.

Contribution

It extends the understanding of Bose gases by determining the ground state energy and low-energy excitations beyond the Gross-Pitaevskii regime for small scattering length parameters.

Findings

Ground state energy computed with vanishing errors as N→∞

Low-energy excitation spectrum characterized in the specified regime

Bridges the gap between Gross-Pitaevskii and thermodynamic limits

Abstract

We consider Bose gases of $N$ particles in a box of volume one, interacting through a repulsive potential with scattering length of order $N^{1-\kappa}$, for $\kappa > 0$. Such regimes interpolate between the Gross-Pitaevskii and thermodynamic limits. Assuming that $\kappa$ is sufficiently small, we determine the ground state energy and the low-energy excitation spectrum of the system, up to errors vanishing in the limit of large $N$.