1. Classical limits for quantum maps on the torus
- Author
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Nathan Salwen, Andrzej Lesniewski, and Ron Rubin
- Subjects
Nonlinear Sciences::Chaotic Dynamics ,Plane (geometry) ,Canonical quantization ,Propagator ,Statistical and Nonlinear Physics ,Torus ,Automorphism ,Quantum ,Unitary state ,Mathematical Physics ,Classical limit ,Mathematics ,Mathematical physics - Abstract
We provide a rigorous canonical quantization for the following toral automorphisms: cat maps, generalized kicked maps, and generalized Harper maps. For each of these systems we construct a unitary propagator and prove the existence of a well-defined classical limit. We also provide an alternative derivation of Hannay and Berry results for the cat map propagator on the plane.
- Published
- 1998
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