I discuss recent results on the effective dynamics of quantum
particles coupled to a dispersive quantum reservoir. In particular, I
discuss some mechanisms for friction by emission of Cerenkov radiation
(zero temperature) and the phenomenon of quantum Brownian motion
(positive temperature), including the Einstein relation. An overview of
results and of models of different degrees of difficulty is given, and some
key ideas going into the proofs of the basic results are indicated.
My talk is based on joint work with Wojciech De Roeck, Alessandro
Pizzo, Israel Michael Sigal and Gang Zhou.