Spectral densities for hot QCD plasmas in a leading log approximation

Abstract

We compute the spectral densities of $T^{μν}$ and $J^μ$ in high temperature QCD plasmas at small frequency and momentum,\, $ω,k \sim g^4 T$. 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.

39 pages, 6 figures. v3 contains an analysis of the bulk channel with non-conformal hydrodynamics. Otherwise no significant changes