SEPARATING THE REGULAR AND IRREGULAR ENERGY-LEVELS AND THEIR STATISTICS IN A HAMILTONIAN SYSTEM WITH MIXED CLASSICAL DYNAMICS

We look at the high-lying eigenstates (from the 10 001 to the 13 000) in the Robnik billiard (defined as a quadratic conformal map of the un it disk) with the shape parameter lambda=0.15. All the 3000 eigenstate s have been numerically calculated and examined in the configuration s pace and in the phase space which-in comparison with the classical pha se space-enabled a clear cut classification of energy levels into regu lar and irregular. This is the first successful separation of energy l evels based on purely dynamical rather than special geometrical symmet ry properties. We calculate the fractional measure of regular levels a s rho(1)=0.365+/-0.01, which is in remarkable agreement with the class ical estimate rho(1)=0.360+/-0.001. This finding confirms the Percival 's (1973) classification scheme, the assumption in Berry-Robnik (1984) theory and the rigorous result by Lazutkin (1981, 1991). The regular levels obey the Poissonian statistics quite well, whereas the irregula r sequence exhibits the fractional power-law level repulsion and globa lly Brody-like statistics with beta=0.286+/-0.001. This is due to the strong localization of irregular eigenstates in the classically chaoti c regions. Therefore, in the entire spectrum we see that the Berry-Rob nik regime is not yet fully established so that the level spacing dist ribution is correctly captured by the Berry-Robnik-Brody distribution.