2012/08/29 by Reika Fukuizumi, Fukuizumi, Reika, Andrea Sacchetti +1
Mathematics · Physics and Astronomy · #35Q55 #81Q20 #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum many-body systems #Quantum, superfluid, helium dynamics #math-ph #math.AP #math.MP #msc:35Q55 #msc:81Q20
paper · pdf · doi:10.48550/arxiv.1208.5867
29 pages; Keywords: Nonlinear Schroedinger and Discrete Nonlinear Schroedinger equations; Semiclassical approximation; Bose-Einstein condensates in periodic lattices
arxiv created 2012/08/29 · openalex publication_date 2012/08/29 · arxiv updated 2012/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider a one-dimensional non-linear Schroedinger equation (NLSE) with a periodic potential. In the semiclassical limit we prove that the stationary solutions of the Bose-Hubbard equation approximate the stationary solutions of the (NLSE). In particular, in the limit of large nonlinearity strength the stationary solutions turn out to be localized on a single lattice site of the periodic potential; as a result the phase transition from superfluid to Mott-insulator phase for Bose-Einstein condensates in a one-dimensional periodic lattice is rigorously proved.