THE UNUSUAL NATURE OF THE QUANTUM BAKER TRANSFORMATION

We investigate the quantum Baker's transformation which has been introduced as a paradigm for studies of the quantum mechanics of classically chaotic systems. A semiclassical theory of the dynamics, good to times logarithmic in h{stroke}, is given in the form of a linear wave packet dynamics. The consequences for the implied heavy eigenfunction scarring and for the trace of the propagator are compared to the quantum results. Unexpectedly, the semiclassical trace remains accurate beyond this logarithmic time. Some exotic quantum properties are found that cannot be explained by the short time semiclassics. Further study reveals level clustering, large recurrences in the trace of the propagator, and excesses of small eigenvector components. Many of the unusual behaviors have a very strong and peculiar h{stroke} dependence. © 1991.