# The Bose gas in a box with Neumann boundary conditions

@inproceedings{Boccato2022TheBG, title={The Bose gas in a box with Neumann boundary conditions}, author={Chiara Boccato and Robert Seiringer}, year={2022} }

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.

## One Citation

### Energy expansions for dilute Bose gases from local condensation results: a review of known results

- Physics
- 2022

Non-relativistic interacting bosons at zero temperature, in two and three dimensions, are expected to exhibit a fascinating critical phase, famously known as condensate phase. Even though a proof of…

## References

SHOWING 1-10 OF 35 REFERENCES

### Bogoliubov Spectrum of Interacting Bose Gases

- Physics
- 2012

We study the large‐N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the next…

### Bogoliubov theory in the Gross-Pitaevskii limit: a simplified approach

- PhysicsForum of Mathematics, Sigma
- 2022

Abstract We show that Bogoliubov theory correctly predicts the low-energy spectral properties of Bose gases in the Gross-Pitaevskii regime. We recover recent results from [6, 7]. While our main…

### Bogoliubov Theory for Trapped Bosons in the Gross–Pitaevskii Regime

- PhysicsAnnales Henri Poincaré
- 2022

We consider systems of N bosons in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

### Bogoliubov excitation spectrum of trapped Bose gases in the Gross-Pitaevskii regime

- Physics
- 2021

We consider an inhomogeneous system of $N$ bosons in $\mathbb{R}^3$ confined by an external potential and interacting via a repulsive potential of the form $N^2 V(N(x-y))$. We prove that the…

### Excitation Spectrum of Bose Gases beyond the Gross–Pitaevskii regime

- PhysicsReviews in Mathematical Physics
- 2022

We consider Bose gases of N particles in a box of volume one, interacting through a repulsive potential with scattering length of order N, for κ > 0. Such regimes interpolate between the…

### Bose–Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross–Pitaevskii Regime

- PhysicsMathematical Physics, Analysis and Geometry
- 2022

We consider a Bose gas consisting of N particles in R, trapped by an external field and interacting through a two-body potential with scattering length of order N. We prove that low energy states…

### A new second-order upper bound for the ground state energy of dilute Bose gases

- PhysicsForum of Mathematics, Sigma
- 2021

Abstract We establish an upper bound for the ground state energy per unit volume of a dilute Bose gas in the thermodynamic limit, capturing the correct second-order term, as predicted by the…

### Another proof of BEC in the GP-limit

- Mathematics
- 2020

We present a fresh look at the methods introduced by Boccato, Brennecke, Cenatiempo, and Schlein concerning the trapped Bose gas and give a conceptually very simple and concise proof of BEC in the…

### Length scales for BEC in the dilute Bose gas

- PhysicsPartial Differential Equations, Spectral Theory, and Mathematical Physics
- 2021

We give a short proof of Bose Einstein Condensation of dilute Bose gases on length scales much longer than the Gross-Pitaevskii scale.

### Bose–Einstein Condensation Beyond the Gross–Pitaevskii Regime

- Materials ScienceAnnales Henri Poincaré
- 2020

It is shown that low-energy states exhibit Bose–Einstein condensation and bounds on the expectation and on higher moments of the number of excitations are provided.