Ground state of Bose gases interacting through singular potentials

TL;DR

This paper analyzes the ground state properties of a Bose gas with singular, scaled interactions, providing a refined correction to the Bogoliubov theory for the system's energy and state.

Contribution

It introduces a next order correction to Bogoliubov theory for Bose gases with singular pair interactions, advancing theoretical understanding.

Findings

Derived the next order correction to the ground state energy.

Established the validity of the correction for a range of interaction parameters.

Enhanced the theoretical framework for analyzing Bose gases with singular potentials.

Abstract

We consider a system of $N$ bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form $N^{3\beta-1} v (N^\beta x)$ for $\beta \in (0,1)$. We prove the next order correction to Bogoliubov theory for the ground state and the ground state energy.