  Magnetic resonance studies of nuclear spins in solids are exceptionally well
suited to probe the limits of statistical physics. We report experimental
results indicating that isolated macroscopic systems of interacting nuclear
spins possess the following fundamental property: spin decays that start from
different initial configurations quickly evolve towards the same long-time
behavior. This long-time behavior is characterized by the shortest ballistic
microscopic timescale of the system and therefore falls outside of the validity
range for conventional approximations of statistical physics. We find that the
nuclear free induction decay and different solid echoes in hyperpolarized solid
xenon all exhibit sinusoidally modulated exponential long-time behavior
characterized by identical time constants. This universality was previously
predicted on the basis of analogy with resonances in classical chaotic systems.
