Thermalization and isotropization of heavy quarks in a non-Markovian medium in high-energy nuclear collisions

We study the isotropization and thermalization of heavy quarks in a non-Markovian medium in high energy nuclear collisions. In particular, we analyze the case of a non-stationary medium with a noise whose time-correlator decays as a power law (heavy tailed noise). We assume the correlations decay with an exponent $\beta-1$, $0\leq\beta<1$; we treat $\beta$ as a free parameter. We analyze the effect of memory on the thermalization and isotropization of heavy quarks in the medium via a generalized Langevin equation. In general, we find that memory slows down the dynamics of heavy quarks; moreover, thermalization and isotropization happen on the same time scale once a realistic initialization is considered. We also find that while the effect on charm quarks can be relevant, beauty quarks are hardly affected by memory in the quark-gluon plasma phase. Finally, we comment on the effect of memory on the estimate of $D_s$ of charm and beauty.