  We investigate the behavior of a pair of heavy fermions, denoted by $Q$ and
$\bar{Q}$, in a hot/dense medium. Although we have in mind the situation where
$Q$ and $\bar{Q}$ denote heavy quarks, our treatment will be limited to
simplified models, which bear only some general similarities with QCD. We study
in particular the limiting case where the mass of the heavy fermions is
infinite. Then a number of results can be derived exactly: a Schr\"odinger
equation can be established for the correlator of the heavy quarks; the
interaction effects exponentiate, leading to a simple instantaneous effective
potential for this Schr\"odinger equation. We consider simple models for the
medium in which the $Q\bar Q$ pair propagates. In the case where the medium is
a plasma of photons and light charged fermions, an imaginary part develops in
this effective potential. We discuss the physical interpretation of this
imaginary part in terms of the collisions between the heavy particles and the
light fermions of the medium; the same collisions also determine the damping
rate of the heavy fermions. Finally we study the connection between the
real-time propagator of the heavy fermion pair and its Euclidean counterpart,
and show that the real part of the potential entering the Schr\"odinger
equation for the real-time propagator is the free energy calculated in the
imaginary-time formalism.
