  We investigate low-temperature dephasing in several model systems, where a
quantum degree of freedom is coupled to a bath. Dephasing, defined as the decay
of the coherence of inital non-equilibrium states, also influences the dynamics
of equilibrium correlation and response functions, as well as static
interference effects. In particular in the latter case dephasing should be
distinguished from renormalization effects. For illustration, and because of
its relevance for quantum state engineering in dissipative environments, we
first reconsider dephasing in spin-boson models. Next we review
Caldeira-Leggett models, with applications, e.g., to persistent currents in
mesoscopic rings. Then, we analyze the more general problem of a particle which
interacts with a quantum field V(t,r(t)), the fluctuations of which are
characterized by a dielectric function epsilon(omega,k). Finally, we compare
this model, both the formulation as well as the results, to the problem of
interacting electrons in a diffusive conductor.
