On the Thomas-Fermi ground state in a harmonic potential

2009/11/19 by Clément Gallo, Gallo, Clément, Dmitry E. Pelinovsky +2
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum many-body systems #Strong Light-Matter Interactions #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.0911.3913

38 pages, no figures

arxiv created 2009/11/19 · openalex publication_date 2009/11/19 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study nonlinear ground states of the Gross-Pitaevskii equation in the space of one, two and three dimensions with a radially symmetric harmonic potential. The Thomas-Fermi approximation of ground states on various spatial scales was recently justified using variational methods. We justify here the Thomas-Fermi approximation on an uniform spatial scale using the Painlevé-II equation. In the space of one dimension, these results allow us to characterize the distribution of eigenvalues in the point spectrum of the Schrödinger operator associated with the nonlinear ground state.

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