CORRESPONDENCE IN QUASI-PERIODIC AND CHAOTIC MAPS - QUANTIZATION VIA THE VON-NEUMANN EQUATION

A generalized approach to the quantization of a large class of maps on a torus, i.e., quantization via the von Neumann equation, is describe d and a number of issues related to the quantization of model systems are discussed. The approach yields well-behaved mixed quantum states f or tori for which the corresponding Schrodinger equation has no soluti ons, as well as an extended spectrum for tori where the Schrodinger eq uation can be solved. Quantum-classical correspondence is demonstrated for the class of mappings considered, with the Wigner-Weyl density rh o(p, q, t) going to the correct classical limit. An application to the cat map yields, in a direct manner, nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the correspondence limit.