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arXiv · 1802.02103

Hyperspherical-LOCV Approximation to Resonant BEC

M. W. C. Sze·A. G. Sykes·D. Blume·J. L. Bohn
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Abstract

We study the ground state properties of a system of $N$ harmonically trapped bosons of mass $m$ interacting with two-body contact interactions, from small to large scattering lengths. This is accomplished in a hyperspherical coordinate system that is flexible enough to describe both the overall scale of the gas and two-body correlations. By adapting the lowest-order constrained variational (LOCV) method, we are able to semi-quantitatively attain Bose-Einstein condensate ground state energies even for gases with infinite scattering length. In the large particle number limit, our method provides analytical estimates for the energy per particle $E_0/N \approx 2.5 N^{1/3} \hbar \omega$ and two-body contact $C_2/N \approx 16 N^{1/6}\sqrt{m\omega/\hbar}$ for a Bose gas on resonance, where $\omega$ is the trap frequency.

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M. W. C. Sze, A. G. Sykes, D. Blume, J. L. Bohn. 2018-02-06. Hyperspherical-LOCV Approximation to Resonant BEC. https://doi.org/10.1103/physreva.97.033608

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