Spectral densities for hot QCD plasmas in a leading log approximation

TL;DR

This paper calculates spectral densities in high-temperature QCD plasmas at small frequencies and momenta, revealing a transition from free streaming particles to hydrodynamics, and determines second order transport coefficients.

Contribution

It reformulates the leading log Boltzmann equation as a Fokker-Planck equation and numerically solves it to analyze spectral densities and transport coefficients in QCD plasmas.

Findings

Spectral densities show a smooth transition from free streaming to hydrodynamics.

All second order transport coefficients are determined.

The transition is analyzed using conformal and non-conformal hydrodynamics.

Abstract

We compute the spectral densities of $T^{\mu\nu}$ and $J^{\mu}$ in high temperature QCD plasmas at small frequency and momentum,\, $\omega,k \sim g^4 T$. The leading log Boltzmann equation is reformulated as a Fokker Planck equation with non-trivial boundary conditions, and the resulting partial differential equation is solved numerically in momentum space. The spectral densities of the current, shear, sound, and bulk channels exhibit a smooth transition from free streaming quasi-particles to ideal hydrodynamics. This transition is analyzed with conformal and non-conformal second order hydrodynamics, and a second order diffusion equation. We determine all of the second order transport coefficients which characterize the linear response in the hydrodynamic regime.