The Bose gas in a box with Neumann boundary conditions

TL;DR

This paper proves Bose-Einstein condensation for a Bose gas in a box with Neumann boundary conditions, providing optimal bounds on condensate depletion and ground state energy, bridging finite and thermodynamic limits.

Contribution

It establishes Bose-Einstein condensation in the Gross-Pitaevskii regime with optimal bounds and connects finite box results to the thermodynamic limit.

Findings

Proves Bose-Einstein condensation in the specified setting.

Provides optimal bounds on condensate depletion.

Derives lower bounds for ground state energy in the thermodynamic limit.

Abstract

We consider a gas of bosonic particles confined in a box with Neumann boundary conditions. We prove Bose-Einstein condensation in the Gross-Pitaevskii regime, with an optimal bound on the condensate depletion. Our lower bound for the ground state energy in the box implies (via Neumann bracketing) a lower bound for the ground state energy of the Bose gas in the thermodynamic limit.