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Beyond Gross-Pitaevskii:local density vs. correlated basis approach for trapped bosons

A. Fabrocini·A. Polls
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Abstract

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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A. Fabrocini, A. Polls. 1999-01-29. Beyond Gross-Pitaevskii:local density vs. correlated basis approach for trapped bosons. https://doi.org/10.1103/physreva.60.2319

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