Quasiclassical Surface of Section Perturbation Theory

Abstract

Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This solves the long standing problem of quantizing the resonances and chaotic regions generically appearing in classical perturbation theory. The result is achieved by expanding the `phase' of the wavefunction in powers of the square root of the small parameter. It gives explicit WKB-like wavefunctions even for systems which classically show hard chaos. We also find analytic solutions to some questions raised recently.

4 pages, LaTeX, 2 figures

References in corpus (5)

• Ray and wave chaos in asymmetric resonant optical cavities
• Directional emission from asymmetric resonant cavities
• Weak Quantum Ergodicity
• Localization in discontinuous quantum systems
• On the Accuracy of the Semiclassical Trace Formula

Cited by in corpus (10)

• Efficient Quantum Computing of Complex Dynamics
• Directional Tunneling Escape from Nearly Spherical Optical Resonators
• Entanglement versus relaxation and decoherence in a quantum algorithm for quantum chaos
• Quantum localization and cantori in chaotic billiards
• Square billiard with a magnetic flux
• Cantori and dynamical localization in the Bunimovich Stadium
• Near integrable systems
• Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations
• Quality factors of deformed dielectric cavities
• Trace Formulas and Bogomolny's Transfer Operator