# Bogoliubov theory in the Gross–Pitaevskii limit

@article{Boccato2018BogoliubovTI, title={Bogoliubov theory in the Gross–Pitaevskii limit}, author={Chiara Boccato and Christian Brennecke and Serena Cenatiempo and Benjamin Schlein}, journal={Acta Mathematica}, year={2018} }

We consider Bose gases consisting of $N$ particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of the order $N^{-1}$(Gross-Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing as $N \to \infty$. Our results confirm Bogoliubov's predictions.

## 74 Citations

### 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…

### The excitation spectrum of the Bose gas in the Gross–Pitaevskii regime

- PhysicsReviews in Mathematical Physics
- 2020

We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy…

### The excitation spectrum of two dimensional Bose gases in the Gross-Pitaevskii regime

- Physics
- 2022

We consider a system of N bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two-body potential, with a scattering length that is exponentially small in N…

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

- PhysicsCommunications in Mathematical Physics
- 2019

We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime. We show that low-energy states exhibit complete Bose–Einstein condensation with an optimal bound on the number of…

### Bose gases in the Gross-Pitaevskii limit: a survey of some rigorous results

- Physics
- 2022

We review some mathematical work on the Bose gas in the Gross-Pitaevskii regime. We start with the classical results by Lieb, Seiringer and Yngvason on the ground state energy and by Lieb and…

### 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…

### Ground state energy of a Bose gas in the Gross–Pitaevskii regime

- PhysicsJournal of Mathematical Physics
- 2022

We review some rigorous estimates for the ground state energy of dilute Bose gases. We start with Dyson’s upper bound, which provides the correct leading order asymptotics for hard spheres.…

### Optimal rate of condensation for trapped bosons in the Gross–Pitaevskii regime

- PhysicsAnalysis & PDE
- 2022

We study the Bose-Einstein condensates of trapped Bose gases in the Gross-Pitaevskii regime. We show that the ground state energy and ground states of the many-body quantum system are correctly…

### Bogoliubov theory for the dilute Fermi gas in three dimensions

- Physics
- 2022

In a dilute system of N fermions with spin 1 / 2 in three dimensions, we study the correlation energy which is given by the diﬀerence between the ground state energy and the energy of the…

### A Simple 2nd Order Lower Bound to the Energy of Dilute Bose Gases

- PhysicsCommunications in Mathematical Physics
- 2020

For a dilute system of non-relativistic bosons interacting through a positive, radial potential v with scattering length a we prove that the ground state energy density satisfies the bound $$e(\rho )…

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