Thermodynamics of non-interacting Bosons in low-dimensional potentials

TL;DR

This paper investigates whether Bose-Einstein condensation occurs in low-dimensional potentials, concluding that despite ground state population onsets, the specific heat remains analytic, indicating no true phase transition.

Contribution

It provides a detailed analysis of thermodynamic behavior in low-dimensional bosonic systems, clarifying the absence of phase transitions in such configurations.

Findings

Ground state population shows sharp onsets at critical temperature

Specific heat remains analytic, indicating no phase transition

Analysis applies to both 1D harmonic and 2D box potentials

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.