The Wake of a Heavy Quark in Non-Abelian Plasmas : Comparing Kinetic Theory and the AdS/CFT Correspondence

Abstract

We compute the non-equilibrium stress tensor induced by a heavy quark moving through weakly coupled QCD plasma at the speed of light and compare the result to N = 4 Super Yang Mills theory at strong coupling. The QCD Boltzmann equation is reformulated as a Fokker-Planck equation in a leading log approximation which is used to compute the induced stress. The transition from nonequilibrium at short distances to equilibrium at large distances is analyzed with first and second order hydrodynamics. Even after accounting for the obvious differences in shear lengths, the strongly coupled theory is significantly better described by hydrodynamics at sub-asymptotic distances. We argue that this difference between the kinetic and AdS/CFT theories is related to the second order hydrodynamic coefficient ${\tau }_{\pi }$. ${\tau }_{\pi }$ is numerically large in units of the shear length for theories based on the Boltzmann equation.

31 pages, 8 figures

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