Excitation spectrum of interacting bosons in the mean-field infinite-volume limit

Abstract

We consider homogeneous Bose gas in a large cubic box with periodic boundary conditions, at zero temperature. We analyze its excitation spectrum in a certain kind of a mean field infinite volume limit. We prove that under appropriate conditions the excitation spectrum has the form predicted by the Bogoliubov approximation. Our result can be viewed as an extension of the result of R. Seiringer (arXiv:1008.5349 [math-ph]) to large volumes.

Revised and extended version. 26 pages, 4 figures. To appear in Annales Henri Poincaré

References in corpus (3)

• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• The ground state energy of a low density Bose gas: a second order upper bound
• The ground state energy of the weakly interacting Bose gas at high density

Cited by in corpus (28)

• Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
• Quantum many-body fluctuations around nonlinear Schrödinger dynamics
• Bogoliubov corrections and trace norm convergence for the Hartree dynamics
• Asymptotic expansion of low-energy excitations for weakly interacting bosons
• Norm approximation for many-body quantum dynamics: focusing case in low dimensions
• Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime
• Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime
• The Bogoliubov free energy functional I. Existence of minimizers and phase diagram
• Classical field theory limit of many-body quantum Gibbs states in 2D and 3D
• Bose particles in a box I. A convergent expansion of the ground state of a three-modes Bogoliubov Hamiltonian
• Ground state energy of mixture of Bose gases
• Ground state energy of a Bose gas in the Gross-Pitaevskii regime
• On Bose-Einstein condensates in the Thomas-Fermi regime
• The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime
• Théorèmes de de Finetti, limites de champ moyen et condensation de Bose-Einstein
• Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit
• Bogoliubov theory for dilute bose gases: the Gross-Pitaevskii Regime
• Binding energy of homogeneous Bose gas
• Bosons in a double well: two-mode approximation and fluctuations
• Validity of Bogoliubov's approximation for translation-invariant Bose gases
• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
• Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas
• Derivation of the Bogoliubov Time Evolution for a Large Volume Mean-field Limit
• Excitation spectrum and quasiparticles in quantum gases. A rigorous approach
• Analysis of fluctuations around non linear effective dynamics
• Ground state energy of Bogoliubov energy functional in the high density limit
• The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime
• Reduced fluctuations for bosons in a double well