Low-energy spectrum and dynamics of the weakly interacting Bose gas

TL;DR

This paper reviews the asymptotic expansion of the low-energy spectrum and dynamics of a weakly interacting Bose gas, extending Bogoliubov theory to all orders in 1/N and analyzing the ground state properties.

Contribution

It provides a comprehensive correction to Bogoliubov theory for the Bose gas, including all orders in 1/N and detailed analysis of the ground state density matrix.

Findings

Asymptotic expansion of the low-energy spectrum

All-order corrections to Bogoliubov theory

Full expansion of the ground state density matrix

Abstract

We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates and dynamics, which provides corrections to Bogoliubov theory to all orders in 1/N. This is based on joint works with S. Petrat, P. Pickl, R. Seiringer and A. Soffer. In addition, we derive a full asymptotic expansion of the ground state one-body reduced density matrix.