Study of regular and irregular states in generic systems

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 h̄ 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. PACS numbers: 02.50.+s, 03.65.-w, 03.65.Ge, 03.65.Sq, 05.40.+j, 05.45.+b Submitted to Journal of Physics A: Mathematical and General e–mails: [email protected], [email protected]. [email protected]