  We study the dynamics of heavy quarks in a thermalized quark-gluon plasma
with a time-correlated thermal noise, $\eta$. In this case it is said that
$\eta$ has memory. We use an integro-differential Langevin equation in which
the memory enters via the thermal noise and the dissipative force. We assume
that the time correlations of the noise decay exponentially on a time scale,
$\tau$, that we treat as a free parameter. We compute the effects of $\tau\neq
0$ on the thermalization time of the heavy quarks, on their momentum broadening
and on the nuclear modification factor. We find that overall memory slows down
the momentum evolution of heavy quarks: in fact, transverse momentum broadening
and the formation of $R_{AA}$ are slowed down by memory and the thermalization
time of the heavy quarks become larger. The potential impact on other
observables is discussed briefly.
