  The quantum dynamics of a classically chaotic model are studied in the
approach to the macroscopic limit. The quantum predictions are compared and
contrasted with the classical predictions of both Newtonian and Liouville
mechanics. The time-domain scaling of the optimal quantum-classical
correspondence is analyzed in detail in the case of both classical theories. In
both cases the correspondence for observable quantities is shown to break down
on a time-scale that increases very slowly (logarithmically) with increasing
system size. In the case of quantum-Liouville correspondence such a short
time-scale does not imply a breakdown of correspondence since the largest
quantum-Liouville differences reached on this time-scale decrease rapidly (as
an inverse power) with increasing system size. Therefore the statistical
properties of chaotic dynamics are, as expected, well described by quantum
theory in the macroscopic limit. In contrast, the largest quantum-Newtonian
differences reached on the log time-scale actually increase in proportion to
the system size. Since the invariance properties of the Hamiltonian impose
functional constraints on the time-varying chaotic coordinates, it is possible
to show, moreover, that if the quantum predictions are believed to describe the
coordinates of individual chaotic systems, then they also predict macroscopic
violations of any kinematic or dynamic constants of the motion. These results
for chaotic systems indicate that a valid description of the time-varying
properties of individual macroscopic bodies is not available within the
standard interpretive framework of quantum theory.
