Bose-Einstein condensation and dissipative dynamics in a relativistic pion gas

Pion condensation in ultrarelativistic 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 BEC in ultrarelativistic heavy-ion collisions. Further, we obtain viscosity ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>η</a:mi> </a:math> ), bulk viscosity ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>ζ</c:mi> </c:math> ), and speed of sound ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>c</e:mi> <e:mi>s</e:mi> </e:msub> </e:math> ) by employing the Boltzmann transport equation with the relaxation time approximation. Findings show a substantial drop in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>η</g:mi> <g:mo>/</g:mo> <g:mi>s</g:mi> </g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>ζ</i:mi> <i:mo>/</i:mo> <i:mi>s</i:mi> </i:math> 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.