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Beyond the Gross-Pitaevskii approximation: Local density versus correlated basis approach for trapped bosons
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We study the ground state of a system of Bose hard-spheres trapped in an isotropic harmonic potential to investigate the effect of the interatomic correlations and the accuracy of the Gross-Pitaevskii equation. We compare a local density approximation, based on the energy functional derived from the low density expansion of the energy of the uniform hard sphere gas, and a correlated wave function approach which explicitly introduces the correlations induced by the potential. Both higher order terms in the low density expansion, beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of the order of percent when the number of trapped particles becomes similar to that attained in recent experiments.
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FABROCINI, A., POLLS MARTÍ, Artur. Beyond the Gross-Pitaevskii approximation: Local density versus correlated basis approach for trapped bosons. _Physical Review A_. 1999. Vol. 60, núm. 3, pàgs. 2319-2323. [consulta: 24 de gener de 2026]. ISSN: 1050-2947. [Disponible a: https://hdl.handle.net/2445/9554]