Coarse grained Liouville dynamics of piecewise linear discontinuous maps

2007/10/23 by M. E. Spina, María E. Spina, Marcos Saraceno +1
Computer Science · Mathematics · Physics and Astronomy · #Dynamics (music) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Physics #Piecewise linear function #Quantum chaos and dynamical systems #nlin.CD #quant-ph

paper · pdf · doi:10.1088/1751-8113/41/10/105402

published in Journal of Physics A Mathematical and Theoretical 41(10), 105402 (Institute of Physics) · 11 pages, 8 figures

arxiv created 2007/10/23 · openalex publication_date 2008/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We compute the spectrum of the classical and quantum mechanical coarse-grained propagators for a piecewise linear discontinuous map. We analyze the quantum - classical correspondence and the evolution of the spectrum with increasing resolution. Our results are compared to the ones obtained for a mixed system.

Citations

• Periodic orbit quantization of a Hamiltonian map on the sphere
• Resonances of the Frobenius-Perron operator for a Hamiltonian map with a mixed phase space
• Hamiltonian mappings and circle packing phase spaces: numerical investigations
• Hamiltonian mappings and circle packing phase spaces
• Quantum Theory of Angular Momentum