  It is predicted that (i) spin echoes have two kinds of generic long-time
decays: either simple exponential, or a superposition of a monotonic and an
oscillatory exponential decays; and (ii) the long-time behavior of spin echo
and the long-time behavior of the corresponding homogeneous free induction
decay are characterized by the same time constants. This prediction extends to
various echo problems both within and beyond nuclear magnetic resonance.
Experimental confirmation of this prediction would also support the notion of
the eigenvalues of time evolution operators in large quantum systems.
