Statistical mechanics and path integrals for a finite number of bosons

TL;DR

This paper examines the statistical mechanics of finite boson systems, highlighting discrepancies caused by approximation errors or misinterpretations, and demonstrates that path integral methods yield consistent results across different calculation approaches.

Contribution

It clarifies the conditions under which path integral methods produce consistent results for finite boson systems and identifies sources of contradictions in previous approaches.

Findings

Path integral methods give consistent results for mean energy, specific heat, and condensation temperature.

Contradictions arise from approximate relations or misinterpretation of the generating function.

The study resolves discrepancies in finite boson statistical mechanics calculations.

Abstract

Recent investigations show that the statistical mechanics of a finite number of particles in ideal harmonic systems predicts different results for the same physical properties, depending on the ensemble under consideration. Path integral methods for a finite number of bosons with equidistant energy levels give the same answers for the mean energy, the specific heat and the condensation temperature etc., irrespective whether their calculation results from the density of states, from the partition function or from the generating function. We show that this contradiction is due either to the use of approximate relations between quantum statistical expressions, or to a misinterpretation of the generating function.