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Regular and Irregular States in Generic Systems

Gregor Veble·Marko Robnik·Junxian Liu
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Abstract

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.

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Gregor Veble, Marko Robnik, Junxian Liu. 2000-03-30. Regular and Irregular States in Generic Systems. https://doi.org/10.1088/0305-4470%2F32%2F36%2F306

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