  We study the motion of a heavy tracer particle weakly coupled to a dense
interacting Bose gas exhibiting Bose-Einstein condensation. In the so-called
mean-field limit, the dynamics of this system approaches one determined by
nonlinear Hamiltonian evolution equations. We derive the effective dynamics of
the tracer particle, which is described by a non-linear integro-differential
equation with memory, and prove that if the initial speed of the tracer
particle is below the speed of sound in the Bose gas the motion of the particle
approaches an inertial motion at constant velocity at large times.
