Canonical Ensemble vs. Grand Canonical Ensemble in the Description of Multicomponent Bosonic Systems

TL;DR

This paper compares the effectiveness of canonical and grand canonical ensembles in describing multicomponent bosonic systems with Bose-Einstein condensates, highlighting limitations of the grand canonical approach.

Contribution

It provides a comparative analysis showing that the grand canonical ensemble is inadequate for systems with condensates, emphasizing the importance of ensemble choice in bosonic thermodynamics.

Findings

Grand canonical ensemble fails to accurately describe condensate systems.

Canonical ensemble provides a more suitable framework for bosonic systems with condensates.

The study considers both zero and nonzero isospin charge cases.

Abstract

The thermodynamics of a system of interacting bosonic particles and antiparticles in the presence of the Bose-Einstein condensate is studied in the framework of the Skyrme-like mean-field model. It is assumed that the total charge density (isospin density) is conserved at all temperatures. Two cases are explicitly considered: zero and nonzero isospin charge of the system. A comparative analysis is carried out using Canonical Ensemble and Grand Canonical Ensemble. It is shown that the Grand Canonical Ensemble is not suitable for describing bosonic systems of particles and antiparticles in the presence of condensate.