Spectral densities for hot QCD plasmas in a leading-log approximation

Abstract

We compute the spectral densities of ${T}^{\ensuremath{\mu}\ensuremath{\nu}}$ and ${J}^{\ensuremath{\mu}}$ in high-temperature QCD plasmas at small frequency and momentum, $\ensuremath{\omega},k~{g}^{4}T$. The leading log Boltzmann equation is reformulated as a Fokker-Planck equation with nontrivial 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 quasiparticles to ideal hydrodynamics. This transition is analyzed with conformal and nonconformal second-order hydrodynamics and a second-order diffusion equation. We determine all of the second-order transport coefficients that characterize the linear response in the hydrodynamic regime.