2013/05/31 by Jan Dereziński, Marcin Napiórkowski
Mathematics · Physics and Astronomy · #Boson #Boundary (topology) #Boundary value problem #Cold Atom Physics and Bose-Einstein Condensates #Excitation #Field (mathematics) #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Mean field theory #Periodic boundary conditions #Physics #Pure mathematics #Quantum electrodynamics #Quantum many-body systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Spectrum (functional analysis) #cond-mat.quant-gas #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1007/s00023-013-0302-4
Revised and extended version. 26 pages, 4 figures. To appear in Annales Henri Poincaré
arxiv created 2013/10/28 · openalex publication_date 2014/01/09 · arxiv updated 2015/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Seiringer (Commun. Math. Phys. 306:565–578, 2011 ) to large volumes.