# Fluctuations in non-ideal pion gas with dynamically fixed particle number

## TL;DR

This paper investigates fluctuations and condensate formation in a non-ideal pion gas with fixed particle number, using a $ ext{ } ext{ }$ interaction model and self-consistent approximations, revealing finite variance at the Bose-Einstein condensation point.

## Contribution

It introduces a model with fixed particle number for a non-ideal pion gas and analyzes fluctuations and condensate formation using self-consistent methods.

## Key findings

- Effective pion mass and thermodynamics are computed above the critical temperature.
- Variance of particle number remains finite at the Bose-Einstein condensation point.
- Non-perturbative interactions prevent divergence of fluctuations.

## Abstract

We consider a non-ideal hot pion gas with the dynamically fixed number of particles in the model with the $\lambda\phi^4$ interaction. The effective Lagrangian for the description of such a system is obtained after dropping the terms responsible for the change of the total particle number. Reactions $\pi^+\pi^-\leftrightarrow\pi^0\pi^0$, which determine the isospin balance of the medium, are permitted. Within the self-consistent Hartree approximation we compute the effective pion mass, thermodynamic characteristics of the system and the variance of the particle number at temperatures above the critical point of the induced Bose-Einstein condensation when the pion chemical potential reaches the value of the effective pion mass. We analyze conditions for the condensate formation in the process of thermalization of an initially non-equilibrium pion gas. The normalized variance of the particle number increases with a temperature decrease but remains finite in the critical point of the Bose-Einstein condensation. This is due to the non-perturbative account of the interaction and is in contrast to the ideal-gas case. In the kinetic regime of the condensate formation the variance is shown to stay finite also.