Late time behavior of non-conformal plasmas

TL;DR

This paper analytically explores how non-conformal strongly coupled plasmas approach thermal equilibrium, revealing how deviations from conformality affect the late-time scaling behavior of temperature and energy density.

Contribution

It provides the first analytic solutions for the late-time expansion of non-conformal plasmas in holography, extending previous conformal results to more realistic models with scale invariance breaking.

Findings

Temperature scales as τ^{-s/4} with s depending on non-conformality parameter X

Generalizes conformal plasma decay rate to non-conformal cases

Includes analysis of potentials with power-law corrections, showing logarithmic effects

Abstract

We determine analytically the dependence of the approach to thermal equilibrium of strongly coupled plasmas on the breaking of scale invariance. The theories we consider are the holographic duals to Einstein gravity coupled to a scalar with an exponential potential. The coefficient in the exponent, $X$, is the parameter that controls the deviation from the conformally invariant case. For these models we obtain analytic solutions for the plasma expansion in the late-time limit, under the assumption of boost-invariance, and we determine the scaling behaviour of the energy density, pressure, and temperature as a function of time. We find that the temperature decays as a function of proper time as $T\sim \tau^{-s/4}$ with $s$ determined in terms of the non-conformality parameter $X$ as $s=4(1-4X^2)/3$. This agrees with the result of Janik and Peschanski, $s=4/3$, for the conformal plasmas and generalizes it to non-conformal plasmas with $X\neq 0$. We also consider more realistic potentials where the exponential is supplemented by power-law terms. Even though in this case we cannot have exact solutions, we are able under certain assumptions to determine the scaling of the energy, that receives logarithmic corrections.