  We present numerical solutions in a one-dimensional setting of quantum master
equations that have been recently derived. We focus on the dynamics of a single
heavy quark-antiquark pair in a Quark-Gluon Plasma in thermal equilibrium, in
the so-called quantum Brownian regime where the temperature of the plasma is
large in comparison with the spacing between the energy levels of the
$Q\bar{Q}$ system. The one-dimensional potential used in the calculations has
been adjusted so as to produce numbers that are relevant for the phenomenology
of the charmonium. The equations are solved using different initial states and
medium configurations. Various temperature regimes are studied and the effects
of screening and collisions thoroughly analyzed. Technical features of the
equations are analyzed. The contributions of the different operators that
control the evolution are discussed as a function of the temperature. Some
phenomenological consequences are addressed.
