Quasiclassical Surface of Section Perturbation Theory

Details Quasiclassical Surface of Section Perturbation Theory Quasiclassical Surface of Section Perturbation Theory

1998-02-24

arxiv.org/abs/chao-dyn/9802019v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, LaTeX, 2 figures

Scientific paper

10.1103/PhysRevE.59.1694

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.

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