Canonical and Microcanonical Ensemble Approaches to Bose-Einstein Condensation: The Thermodynamics of Particles in Harmonic Traps

TL;DR

This paper analyzes the thermodynamics of bosons in harmonic traps across different ensembles, providing exact calculations of thermodynamic functions and phase transition signals, with brief discussion on fermionic systems.

Contribution

It introduces combinatorial techniques to exactly compute thermodynamic properties of bosons in harmonic traps in various ensembles, highlighting phase transition signals.

Findings

Exact thermodynamic functions computed for bosons in harmonic traps

Clear signals of phase transition observed in occupation numbers

Brief discussion on extending methods to fermionic systems

Abstract

The thermodynamic properties of bosons moving in a harmonic trap in an arbitrary number of dimensions are investigated in the grand canonical, canonical and microcanonical ensembles by applying combinatorial techniques developed earlier in statistical nuclear fragmentation models. Thermodynamic functions such as the energy and specific heat are computed exactly in these ensembles. The occupation of the ground or condensed state is also obtained exactly, and signals clearly the phase transition. The application of these techniques to fermionic systems is also briefly discussed.