Eur. Phys. J. B 68, 457-465 (2009)
https://doi.org/10.1140/epjb/e2009-00112-9

Systematic semiclassical expansion for harmonically trapped ideal Bose gases

¹ Arnold Sommerfeld Center for Theoretical Physics, Fakultät für Physik, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany
² Universität Duisburg-Essen, Fachbereich Physik, Campus Duisburg, Lotharstrasse 1, 47057 Duisburg, Germany

Corresponding author: ^a axel.pelster@uni-due.de

Received: 30 July 2008
Revised: 19 January 2009
Published online: 25 March 2009

Abstract

Using a field-theoretic approach, we systematically generalize the usual semiclassical approximation for a harmonically trapped ideal Bose gas in such a way that its range of applicability is essentially extended. With this we can analytically calculate thermodynamic properties even for small particle numbers. In particular, it now becomes possible to determine the critical temperature as well as the temperature dependence of both heat capacity and condensate fraction in low-dimensional traps, where the standard semiclassical approximation is not even applicable.