Regular and Irregular States in Generic Systems

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.