1993/11/16 by Joshua Wilkie, Paul Brumer · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Chaotic #Classical limit #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematical physics #Mathematics #Physics #Propagator #Quantization (signal processing) #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Quasiperiodic function #Torus #chao-dyn #nlin.CD
paper · pdf · doi:10.1103/physreve.49.1968
36 pages, RevTex preprint format
arxiv created 1993/11/16 · openalex publication_date 1994/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A generalized approach to the quantization of a large class of maps on a torus, i.e., quantization via the von Neumann equation, is described and a number of issues related to the quantization of model systems are discussed. The approach yields well-behaved mixed quantum states for tori for which the corresponding Schr"odinger equation has no solutions, as well as an extended spectrum for tori where the Schr"odinger equation can be solved. Quantum-classical correspondence is demonstrated for the class of mappings considered, with the Wigner-Weyl density p(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.