Ideal Boson Particle-Antiparticle System at Finite Temperatures

TL;DR

This paper investigates the thermodynamics of an ideal bosonic particle-antiparticle system at finite temperatures, revealing a charge-dependent second-order phase transition to a Bose-Einstein condensate and discussing potential experimental signals.

Contribution

It introduces a formal framework for incorporating exact charge conservation into the thermodynamics of bosonic systems and analyzes the phase transition behavior at finite temperature.

Findings

A second-order phase transition to Bose-Einstein condensate occurs at a critical temperature T_c.

Condensate forms in the component with the dominant particle number density.

Symmetry breaking at T=0 is a first-order transition induced by particle injection.

Abstract

The thermodynamic properties of an ideal bosonic system composed of particles and antiparticles at finite temperatures are examined within the framework of a scalar field model. It is assumed that particle-antiparticle pair creation occurs; however, the system is simultaneously subject to exact charge (isospin) conservation. To implement this constraint, we first consider the system within the Grand Canonical Ensemble and then transform to the Canonical Ensemble using a Legendre transformation. This procedure provides a formally consistent scheme for incorporating the chemical potential at the microscopic level into the Canonical Ensemble framework. To enforce exact conservation of charge (isospin, N_I), we further analyze the thermodynamic properties of the system within the extended Canonical Ensemble, in which the chemical potential becomes a thermodynamic function of the temperature and conserved charge. It is shown that as the temperature decreases, the system undergoes a second-order phase transition to a Bose-Einstein condensate at the critical temperature T_c, but only when the conserved charge is finite, N_I=const \ne 0. In a particle-antiparticle system, the condensate forms exclusively in the component with the dominant particle number density, which determines the excess charge. We demonstrate that the symmetry breaking of the ground state at T=0 results from a first-order phase transition associated with the formation of a Bose-Einstein condensate. Although the transition involves symmetry breaking, it is not spontaneous in the strict field-theoretic sense, but is instead induced by the external injection of particles. Potential experimental signals of Bose-Einstein condensation of pions produced in high-energy nuclear collisions are briefly discussed.