  Classically chaotic systems relax to coarse grained states of equilibrium.
Here we numerically study the quantization of such bounded relaxing systems, in
particular the quasi-periodic fluctuations associated with the correlation
between two density operators. We find that when the operators, or their
Wigner-Weyl transforms, have obvious classical limits that can be interpreted
as piecewise continuous functions on phase space, the variance of the
fluctuations can distinguish classically chaotic and regular motions, thus
providing a novel diagnostic devise of quantum chaos. We uncover several
features of the relaxation fluctuations that are shared by disparate systems
thus establishing restricted universality. If we consider the nonlinearity
driving the chaos as pseudo-time, we find that the onset of classical chaos is
indicated quantally as the relaxation of the relaxation fluctuations to a
Gaussian distribution.
