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Article Dans Une Revue Asymptotic Analysis Année : 2011

On the Thomas-Fermi ground state in a harmonic potential

Résumé

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 Painlev ́-II equation. In the space of one dimension, these results allow us to characterize e the distribution of eigenvalues in the point spectrum of the Schr ̈dinger operator associated with the nonlinear ground state.
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Dates et versions

hal-00802337 , version 1 (19-03-2013)

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Clément Gallo, Dmitry E. Pelinovsky. On the Thomas-Fermi ground state in a harmonic potential. Asymptotic Analysis, 2011, 73 (1-2), pp.53-96. ⟨10.3233/ASY-2011-1034⟩. ⟨hal-00802337⟩
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