Condensation of Ideal Bose Gas Confined in a Box Within a Canonical Ensemble

TL;DR

This paper analyzes the Bose-Einstein condensation of non-interacting bosons in a box potential within a canonical ensemble, providing new recursion relations and a semiclassical approach that improves upon previous theories.

Contribution

It introduces recursion relations for the partition function and ground-state occupancy, and develops a semiclassical method that accurately captures small-temperature behavior.

Findings

Correct small-T behavior in specific heat and ground state occupancy

Comparison shows improved accuracy over earlier theories

Finite-size effects are quantitatively derived

Abstract

We set up recursion relations for the partition function and the ground-state occupancy for a fixed number of non-interacting bosons confined in a square box potential and determine the temperature dependence of the specific heat and the particle number in the ground state. A proper semiclassical treatment is set up which yields the correct small-T-behavior in contrast to an earlier theory in Feynman's textbook on Statistical Mechanics, in which the special role of the ground state was ignored. The results are compared with an exact quantum mechanical treatment. Furthermore, we derive the finite-size effect of the system.