  An overview is given of the long-time and long-distance behavior of
correlation functions in both classical and quantum statistical mechanics.
After a simple derivation of the classical long-time tails in equilibrium time
correlation functions, we discuss analogous long-distance phenomena in
nonequilibrium classical systems. The paper then draws analogies between these
phenomena and similar effects in quantum statistical mechanics, with emphasis
on the soft modes that underly long-time tails and related phenomena. We also
elucidate the interplay between critical phenomena and long-time tails, using
the classical liquid-gas critical point and the quantum ferromagnetic
transition as examples.
