Thermodynamics of non-interacting bosons in low-dimensional potentials
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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.
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