Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2000-03-29
J. Phys. A: Math. Gen. 32 (1999) 6423-6444
Nonlinear Sciences
Chaotic Dynamics
25 pages, 14 figures (as .GIF files), high quality figures available upon request
Scientific paper
10.1088/0305-4470/32/36/306
In this work we present the results of a numerical and semiclassical analysis of high lying states in a Hamiltonian system, whose classical mechanics is of a generic, mixed type, where the energy surface is split into regions of regular and chaotic motion. As predicted by the principle of uniform semiclassical condensation (PUSC), when the effective $\hbar$ tends to 0, each state can be classified as regular or irregular. We were able to semiclassically reproduce individual regular states by the EBK torus quantization, for which we devise a new approach, while for the irregular ones we found the semiclassical prediction of their autocorrelation function, in a good agreement with numerics. We also looked at the low lying states to better understand the onset of semiclassical behaviour.
Liu Jun-xian
Robnik Marko
Veble Gregor
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