Bose-Einstein Condensation in the Relativistic Pion Gas: Thermodynamic Limit and Finite Size Effects

TL;DR

This paper investigates Bose-Einstein condensation in a relativistic pion gas, analyzing the thermodynamic limit and finite size effects, and discusses potential experimental signals in high-energy collisions.

Contribution

It provides a detailed analysis of BEC in a relativistic pion gas, including finite size effects and fluctuation behavior near the phase transition.

Findings

Fluctuation variance converges in the normal phase for large volumes.

Variance diverges at the BEC transition line, indicating critical behavior.

Finite size effects are significant for experimental detection in high-energy collisions.

Abstract

We consider the Bose-Einstein condensation (BEC) in a relativistic pion gas. The thermodynamic limit when the system volume $V$ goes to infinity as well as the role of finite size effects are studied. At $V\to \infty$ the scaled variance for particle number fluctuations, $\omega=< \Delta N^2>/< N>$, converges to finite values in the normal phase above the BEC temperature, $T>T_C$. It diverges as $\omega \propto V^{1/3}$ at the BEC line $T=T_C$, and $\omega \propto V$ at $T<T_C$ in a phase with the BE condensate. Possible experimental signals of the pion BEC in finite systems created in high energy proton-proton collisions are discussed.