Bose-Einstein Condensation and Dissipative Dynamics in a Relativistic Pion Gas

TL;DR

This paper explores how Bose-Einstein condensation in a relativistic pion gas affects its dissipative properties and equation of state in ultra-relativistic heavy-ion collisions, revealing significant reductions in viscosities and sound speed.

Contribution

It provides a theoretical analysis of dissipative dynamics and finite-size effects of pion BEC using the Boltzmann transport equation with new insights into system size dependence.

Findings

Viscosity to entropy ratio decreases with increased condensation

Speed of sound decreases, indicating softening of the equation of state

Larger systems show more pronounced BEC signatures

Abstract

Pion condensation in ultra-relativistic collisions presents a compelling theoretical phenomenon with significant implications for the dynamics of hadronic matter. Various theoretical frameworks offer insight into the nature of high-temperature Bose-Einstein condensation (BEC). The present study investigates the dissipative behavior of a relativistic pion gas undergoing Bose-Einstein condensation (BEC) in ultra-relativistic heavy-ion collisions. Further, we obtain viscosity ($\eta$), bulk viscosity ($\zeta$), and speed of sound ($c_s$) by employing the Boltzmann transport equation with the relaxation time approximation. Findings show a substantial drop in $\eta/s$ and $\zeta/s$ with the fractional increase in condensation. This effect is becoming more evident in larger systems approaching the thermodynamic limit. Alongside the reduction in viscosities, the speed of sound also decreases with increasing condensation, indicating a softening of the equation of state. The analysis of finite-size effects reveals that larger systems exhibit more pronounced signatures of BEC. These results suggest that pion condensation can influence the hydrodynamic evolution of the hadronic phase in heavy-ion collisions, with consequential implications for interpreting collective flow observables and the underlying equation of state.