Termalizzazione degli Heavy Quarks nel Quark-Gluon Plasma

We investigate the thermalization of heavy quarks (charm and beauty) in heavy-ion collisions. We employ the Langevin equation in order to study the kinetics of heavy quarks in a thermal medium. The equation is solved numerically in simple cases in which the corresponding hydrodynamic equations describing the background medium admit analytical solutions. In particular, we first study the evolution in a static medium; secondly, we include the more realistic case of an expanding fireball. This is done both in a purely longitudinal expansion along the beam axis (Bjorken flow) and in one occurring also in the transverse plane (Gubser flow). In each case we vary the transport coefficients entering into the Langevin equation in order to see whether the heavy quarks reach thermalization before hadronization occurs.