Quantum corrections to the semiclassical Hartree-Fock theory of a harmonically trapped Bose gas

• Published in: The European physical journal. D, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2012, Vol.66 (8), p.203, Article 203
• Main Authors: Schumayer, D., Cormack, S., van Zyl, B.P., Farry, J., Collin, A., Zaremba, E., Hutchinson, D.A.W.
• Format: Article
• Language: English
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Atomic; Atomic and molecular physics; Atomic properties and interactions with photons; Boson systems; Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations); Classical and quantum physics: mechanics and fields; Density-functional theory; Electronic structure of atoms, molecules and their ions: theory; Exact sciences and technology; Matter waves; Molecular; Optical and Plasma Physics; Optical cooling of atoms; trapping; Photon interactions with atoms; Physical Chemistry; Physics; Physics and Astronomy; Quantum Information Technology; Quantum Physics; Quantum statistical mechanics; Regular Article; Spectroscopy/Spectrometry; Spintronics; Statistical physics, thermodynamics, and nonlinear dynamical systems
• ISSN: 1434-6060; 1434-6079; 1434-6079
• DOI: 10.1140/epjd/e2012-30225-y

. Using the phase-space expansion of the thermodynamical distribution functions we provide a general and systematic method for including effects beyond the local-density approximation to the semiclassical Hartree-Fock theories. We illustrate the method by applying it to the case of a strictly two-dimensional, harmonically trapped Bose gas. Thereby, we address the ambiguous prediction of the Hartree-Fock approximation, namely, whether a fixed number of trapped atoms undergoes Bose-Einstein condensation or not. We also investigate the dependence of the critical temperature on the interaction strength.