Quantum corrections to the ground state energy of a trapped Bose-Einstein condensate: A diffusion Monte Carlo calculation
arXiv:cond-mat/0009220 · doi:10.1103/PhysRevA.63.063601
Abstract
The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, [n(0): peak density, a: s-wave scattering length], our calculations confirm that the exact ground state energy for a sum of two-body interactions depends on only the atomic physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for N=2-50 particles in the trap with positive s-wave scattering length a=100-10000 a.u.. Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see e.g. E. Braaten and A. Nieto, Phys. Rev. B 56}, 14745 (1997)], leads to a greatly improved description of trapped Bose gases.
7 pages, 4 figures
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