1997/07/18 by Eric Braaten, Agustin Nieto · 1 citation
Physics and Astronomy · #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1103/physrevb.56.14745
published as Phys.Rev.B56:14745-14765,1997 · 36 pages, 8 figures
arxiv created 1997/07/18 · arxiv updated 2009/11/30
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/√(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.