Periodic orbit quantization of a Hamiltonian map on the sphere

2001/02/28 by A. J. Scott, A J Scott, G. J. Milburn +1 · 2 citations
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Hamiltonian (control theory) #Hamiltonian system #Mathematical Dynamics and Fractals #Orbit (dynamics) #Periodic orbits #Phase space #Quantization (signal processing) #Quantum chaos and dynamical systems #Semiclassical physics #math-ph #math.MP #nlin.CD

paper · pdf · doi:10.1088/0305-4470/34/37/309

published as J. Phys. A 34, 7541 (2001) · 23 pages, REVTEX4

arxiv created 2001/07/10 · openalex publication_date 2001/09/10 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semi-classical quantization of one of these maps.

Citations

• Periodic Orbits and Classical Quantization Conditions
• Boundary contributions to the semiclassical traces of the baker's map
• Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
• Hamiltonian mappings and circle packing phase spaces

Cited by

• Hamiltonian mappings and circle packing phase spaces: numerical investigations
• Coarse grained Liouville dynamics of piecewise linear discontinuous maps