Classical and quantal morphology of a piecewise-linear standard map
- 1 March 1991
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 43 (6) , 3183-3186
- https://doi.org/10.1103/physreva.43.3183
Abstract
We consider a standard map with a continuous, piecewise-linear forcing term. The piecewise linearity allows for an extremely accurate calculation of the classical manifolds and associated homoclinic tangles. A simple coding for the periodic orbits is another useful property of the map. The quantized map is then studied and the resolution of stable and unstable invariant classical structures by the quantum eigenstates is assessed.Keywords
This publication has 17 references indexed in Scilit:
- Role of ‘‘scars’’ in the suppression of ionization in intense, high-frequency fieldsPhysical Review Letters, 1990
- Chaos in Classical and Quantum MechanicsPublished by Springer Nature ,1990
- Inhibition of quantum transport due to ‘‘scars’’ of unstable periodic orbitsPhysical Review Letters, 1989
- On the quantisation of homoclinic motionNonlinearity, 1989
- Quantum mechanics of a classically chaotic system: Observations on scars, periodic orbits, and vibrational adiabaticityPhysical Review A, 1989
- Classical-Quantum Correspondence in the Presence of Global ChaosPhysical Review Letters, 1988
- Quantum mechanics of classically non-integrable systemsPhysics Reports, 1988
- Relevance of classical chaos in quantum mechanics: The hydrogen atom in a monochromatic fieldPhysics Reports, 1987
- Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic OrbitsPhysical Review Letters, 1984
- Chaos, Quantum Recurrences, and Anderson LocalizationPhysical Review Letters, 1982