Effects of Tsallis distribution on parametric resonance in chiral phase transitions

TL;DR

This study investigates how the Tsallis distribution's parameters influence parametric resonance during chiral phase transitions, revealing that the entropic index and temperature significantly affect mode amplification.

Contribution

It introduces the analysis of parametric resonance in chiral transitions considering Tsallis distribution parameters, highlighting their impact on mode amplification in different expansion scenarios.

Findings

Larger q values soften amplified modes in resonance bands.

Amplified modes decrease and vanish with increasing temperature in expansionless case.

Strong amplification occurs around the first resonance band at T=0 in expansion case.

Abstract

The parametric resonance was studied in chiral phase transitions when the momentum distribution is described by a Tsallis distribution. A Tsallis distribution has two parameters, the temperature $T$ and the entropic index $q$. The amplification was estimated in two cases: 1) expansionless case and 2) one dimensional expansion case. In an expansionless case, the temperature $T$ is constant, and the amplified modes as a function of $T$ were calculated for various $q$. In one dimensional expansion case, the temperature $T$ decreases as a function of the proper time, and the amplification as a function of the transverse momentum was calculated for various $q$. In the expansionless case, the following facts were found: 1) the larger the value $q$ is, the softer the amplified modes are for the first and second resonance bands, 2) the amplified mode of the first resonance band decreases and vanishes, as the temperature $T$ increases, and 3) the amplified mode of the second resonance band decreases and approaches to zero, as the temperature $T$ increases. In one dimensional expansion case, the following facts were found: 1) the soft mode is amplified, 2) the amplification is extremely strong around the amplified mode of the first resonance band at $T=0$, and 3) the magnitude of the amplification as a function of transverse momentum oscillates around the amplified mode of the first resonance band at $T=0$.