paper

Quantum Corrections to the Ground State of a Trapped Bose-Einstein Condensate

arXiv:cond-mat/9707199 · doi:10.1103/PhysRevB.56.14745

Abstract

In the mean-field approximation, the number density ρ(r) for the ground state of a Bose-Einstein condensate trapped by an external potential V(r) satisfies a classical field equation called the Gross-Pitaevskii equation. We show that quantum corrections to ρare dominated by quantum fluctuations with wavelengths of order 1/\sqrt{ρa}, where a is the S-wave scattering length. By expanding the equations for the Hartree-Fock approximation to second order in the gradient expansion, we derive local correction terms to the Gross-Pitaevskii equation that take into account the dominant effects of quantum fluctuations. We also show that the gradient expansion for the density breaks down at fourth order.

36 pages, 8 figures

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