SUPPLEMENT TO THE PAPER: Separating the regular and irregular energy levels and their statistics in Hamiltonian system with mixed classical dynamics

Abstract

As a technical supplement to the above mentioned paper we present 192 consecutive eigenstates for the Robnik billiard with the shape parameter $λ=0.15$ from 10,001st to 10,192nd, by showing the plots in the configuration space and in the phase space. The latter is smoothed projection of the Wigner function onto the surface of section. By comparison with the classical SOS plots we thus examine all eigenstates and classify them in regular and irregular: There are 70 regular states and 122 irregular states, thus giving the estimate of the relative measure of the regular component $ρ_1=0.365$, which is in excellent agreement with the classical value $ρ_1=0.360$ calculated and reported by Prosen and Robnik (1993).