  Mathematical results on some models describing the motion of a tracer
particle through a Bose-Einstein condensate are described. In the limit of a
very dense, very weakly interacting Bose gas and for a very large particle
mass, the dynamics of the coupled system is determined by classical non-linear
Hamiltonian equations of motion. The particle's motion exhibits deceleration
corresponding to friction (with memory) caused by the emission of Cerenkov
radiation of gapless modes into the gas.
  Precise results are stated and outlines of proofs are presented. Some
technical details are deferred to forthcoming papers.
