  We discuss the importance of the real part of the Feynman-Vernon influence
action for the analysis of dephasing and decay near the ground state of a
system which is coupled to a bath. Using exactly solvable linear quantum
dissipative systems, it is shown how the effects of the real and the imaginary
part (describing friction and fluctuations, respectively) may cancel beyond
lowest-order perturbation theory. The resulting picture is extended to a
qualitative discussion of nonlinear systems and dephasing of degenerate
fermions. We explain why dephasing rates will, in general, come out finite at
zero temperature if they are deduced from the imaginary part of the action
alone, a procedure which is reliable only for highly excited states.
