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24 April 2024 |
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Variational study of a dilute Bose condensate in a harmonic trap | | Alexander L. Fetter
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25 Jul 1996 | | Subject: | cond-mat | | Abstract: | A two-parameter trial condensate wave function is used to find an approximate variational solution to the Gross-Pitaevskii equation for $N_0$ condensed bosons in an isotropic harmonic trap with oscillator length $d_0$ and interacting through a repulsive two-body scattering length $a>0$. The dimensionless parameter ${cal N}_0 equiv N_0a/d_0$ characterizes the effect of the interparticle interactions, with ${cal N}_0 ll 1$ for an ideal gas and ${cal N}_0 gg 1$ for a strongly interacting system (the Thomas-Fermi limit). The trial function interpolates smoothly between these two limits, and the three separate contributions (kinetic energy, trap potential energy, and two-body interaction energy) to the variational condensate energy and the condensate chemical potential are determined parametrically for any value of ${cal N}_0$, along with illustrative numerical values. The straightforward generalization to an anisotropic harmonic trap is considered briefly. | | Source: | arXiv, cond-mat/9607177 | | Services: | Forum | Review | PDF | Favorites | |
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