Thermodynamics of non-interacting Bosons in low-dimensional potentials

G.-L. Ingold and A. Lambrecht

Eur. Phys. J. D 1, 29–32 (1998) DOI: 10.1007/s100530050060

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.