  Recent theoretical work on the role of microscopic chaos in the dynamics and
relaxation of many-body quantum systems has made several experimentally
confirmed predictions about the systems of interacting nuclear spins in solids,
focusing, in particular, on the shapes of spin echo responses measured by
nuclear magnetic resonance (NMR). These predictions were based on the idea that
the transverse nuclear spin decays evolve in a manner governed at long times by
the slowest decaying eigenmode of the quantum system, analogous to a chaotic
resonance in a classical system. The present paper extends the above
investigations both theoretically and experimentally. On the theoretical side,
the notion of chaotic eigenmodes is used to make predictions about the
relationships between the long-time oscillation phase of the nuclear free
induction decay (FID) and the amplitudes and phases of spin echoes. On the
experimental side, the above predictions are tested for the nuclear spin decays
of F-19 in CaF2 crystals and Xe-129 in frozen xenon. Good agreement between the
theory and the experiment is found.
