Quantum evolution of heavy quarks in the thermal medium

Heavy-flavor particles are excellent probes of the strongly coupled QGP (sQGP). The large heavy-quark (HQ) masses are commonly believed to warrant a semiclassical transport approach to simulate their motion in the fireball as formed in ultra-relativistic heavy-ion collisions. However, large collision rates in the sQGP, approaching 0.5-1 GeV, raise the issue of quantum effects in the HQ transport, especially for charm. Here, we employ the quantum Boltzmann equation to investigate this question. We employ the Lindblad formalism to compute the time evolution of the HQ density matrix to compare the relaxation behavior with classical Langevin simulations, in particular differences in the spatial diffusion coefficients. In-medium spectral functions of thermal partons (taken from a self-consistent T-Matrix formalism) are employed to implement off-shell effects into Monte Carlo simulations of the density matrices, and different HQ coupling strengths to the medium are considered. The lower bound for the spatial diffusion coefficients in the strong coupling limit is also studied.