THERMODYNAMICS OF NONINTERACTING BOSONS IN LOW-DIMENSIONAL POTENTIALS

On the basis of a macroscopic ground state population it was argued re cently that Bose-Einstein condensation should occur in a one-dimension al harmonic potential. We examine this situation by drawing analogies to bosons in a two-dimensional box, where the thermodynamic limit is w ell-defined. We show that in both systems although the ground state po pulations 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.