Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

TL;DR

This paper derives a detailed two-term expansion of the ground state one-body density matrix for a mean-field Bose gas, enhancing understanding of quantum many-body systems in the large particle limit.

Contribution

It introduces a cubic correction to Bogoliubov's approximation, providing a more precise description of the ground state properties of the Bose gas.

Findings

Two-term expansion of the one-body density matrix derived

Enhanced accuracy over traditional Bogoliubov approximation

Applicable in the mean-field limit for large particle numbers

Abstract

We consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov's approximation of the ground state energy and the ground state.