https://doi.org/10.1140/epjd/e2012-30225-y
Regular Article
Quantum corrections to the semiclassical Hartree-Fock theory of a harmonically trapped Bose gas
1
Meteorological Service of New Zealand Ltd., 30 Salamanca Road, 6012
Wellington, New
Zealand
2
Jack Dodd Centre for Quantum Technology, University of
Otago, 9016
Dunedin, New
Zealand
3
Department of Physics, St. Francis Xavier
University, Antigonish,
Nova Scotia
2W5 B2G,
Canada
4
NORDITA, 106
91
Stockholm,
Sweden
5
Department of Physics, Queen’s University, 99 University Avenue
Kingston, K7L 3N6
Ontario,
Canada
6
Centre for Quantum Technologies, National University of
Singapore, 2 Science Drive
3, 117543
Singapore,
Singapore
a e-mail: daniel.schumayer@gmail.com
Received:
21
October
2011
Received in final form:
12
May
2012
Published online:
16
August
2012
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.
Key words: Cold Matter and Quantum Gas
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2012
