Spectral densities for hot QCD plasmas in a leading log approximation

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.

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