The ground state energy of the weakly interacting Bose gas at high density

TL;DR

This paper rigorously proves the Lee-Huang-Yang formula for the ground state energy of a 3D weakly interacting Bose gas at high density, confirming the accuracy of the Bogoliubov approximation in this regime.

Contribution

It provides a rigorous mathematical proof of the Lee-Huang-Yang formula for the Bose gas in a specific high-density, weak-coupling limit, validating the Bogoliubov approximation.

Findings

Proves the Lee-Huang-Yang formula for the ground state energy.

Shows the Bogoliubov approximation is exact in the considered regime.

Validates theoretical predictions for high-density Bose gases.

Abstract

We prove the Lee-Huang-Yang formula for the ground state energy of the 3D Bose gas with repulsive interactions described by the exponential function, in a simultaneous limit of weak coupling and high density. In particular, we show that the Bogoliubov approximation is exact in an appropriate parameter regime, as far as the ground state energy is concerned.