2008/06/21 by Clément Gallo, Gallo, Clément, Dmitry E. Pelinovsky +2
Computer Science · Mathematics · Physics and Astronomy · #35P20 #35Q51 #35Q55 #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum many-body systems #math-ph #math.MP #msc:35P20 #msc:35Q51 #msc:35Q55
paper · pdf · doi:10.48550/arxiv.0806.3516
arxiv created 2008/06/21 · openalex publication_date 2008/06/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a nonlinear ground state of the Gross-Pitaevskii equation with a parabolic potential in the hydrodynamics limit often referred to as the Thomas--Fermi approximation. Existence of the energy minimizer has been known in literature for some time but it was only recently when the Thomas-Fermi approximation was rigorously justified. The spectrum of linearization of the Gross-Pitaevskii equation at the ground state consists of an unbounded sequence of positive eigenvalues. We analyze convergence of eigenvalues in the hydrodynamics limit. Convergence in norm of the resolvent operator is proved and the convergence rate is estimated. We also study asymptotic and numerical approximations of eigenfunctions and eigenvalues using Airy functions.