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Thermalization of a heavy quark near rest is controlled by the correlator oftwo electric fields along a temporal Wilson line. We address this correlatorwithin real-time, classical lattice Yang-Mills theory, and elaborate on theanalogies that exist with the dynamics of hot QCD. In the weak-coupling limit,it can be shown analytically that the dynamics on the two sides are closelyrelated to each other. For intermediate couplings, we carry outnon-perturbative simulations within the classical theory, showing that theleading term in the weak-coupling expansion significantly underestimates theheavy quark thermalization rate. Our analytic and numerical results also yielda general understanding concerning the overall shape of the spectral functioncorresponding to the electric field correlator, which may be helpful insubsequent efforts to reconstruct it from Euclidean lattice Monte Carlosimulations.

Heavy Quark Thermalization in Classical Lattice Gauge Theory: Lessons for Strongly-Coupled QCD