Langevin dynamics and decoherence of heavy quarks at high temperatures

A Langevin equation of heavy quarks in high-temperature quark-gluon plasma is derived. The dynamics of heavy quark color is coupled with the phase space dynamics and causes a macroscopic superposition state of heavy quark momentum. Decoherence of the superposition state allows one to use a classical description. The time scale of decoherence gives an appropriate discretization time scale $\Delta t\sim \sqrt{M/C_{\rm F}\gamma}$ for the classical Langevin equation, where $M$ is heavy quark mass and $\gamma$ is heavy quark momentum diffusion constant.