Eur. Phys. J. D 1, 29-32 (1998)
https://doi.org/10.1007/s100530050060

Thermodynamics of non-interacting bosons in low-dimensional potentials

¹ Institut für Physik, Universität Augsburg, Memminger Str. 6, 86135 Augsburg, Germany
² Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany

Corresponding authors: ^a gert.ingold@physics.uni-augsburg.de - ^b astrid@spectro.jussieu.fr

Received: 17 February 1997
Revised: 3 September 1997
Accepted: 13 October 1997
Published online: 15 January 1998

Abstract

On the basis of a macroscopic ground state population it was argued recently that Bose-Einstein condensation should occur in a one-dimensional harmonic potential. We examine this situation by drawing analogies to bosons in a two-dimensional box, where the thermodynamic limit is well-defined. We show that in both systems although the ground state populations show sharp onsets at the critical temperature, the behaviour of the specific heat is analytic, which proves the absence of a phase transition in these systems.