Diagonalizing Bose Gases in the Gross-Pitaevskii Regime and Beyond

TL;DR

This paper introduces a new method for analyzing dilute Bose gases, deriving key formulas and extending spectral results beyond traditional regimes, with implications for understanding quantum many-body systems.

Contribution

It provides an elementary derivation of the Lee-Huang-Yang formula and extends excitation spectrum analysis to more singular regimes beyond the Gross-Pitaevskii scaling.

Findings

Elementary derivation of Lee-Huang-Yang formula

Extension of excitation spectrum results

Upper bound on ground state energy

Abstract

We present a novel approach to the Bogoliubov theory of dilute Bose gases, allowing for an elementary derivation of the celebrated Lee-Huang-Yang formula in the Gross-Pitaevskii regime. Furthermore, we identify the low lying excitation spectrum beyond the Gross-Pitaevskii scaling, extending a recent result [3] to significantly more singular scaling regimes. Finally, we provide an upper bound on the ground state energy in the Gross-Pitaevskii regime that captures the correct expected order of magnitude beyond the Lee-Huang-Yang formula.