POLYGONAL BILLIARDS - CORRESPONDENCE BETWEEN CLASSICAL TRAJECTORIES AND QUANTUM EIGENSTATES

Correspondence between classical trajectories and quantum eigenstates in polygonal billiards is studied. Level statistics of polygonal billi ards are close to GOE-type fluctuation but they depend weakly on the e nergy. Among the eigenfunctions with quite irregular patterns which ca nnot be distinguished from typical patterns of classical chaotic billi ards, there are regular eigenfunctions each of which is associated wit h a certain classical counterpart. Moreover, some of regular eigenstat es do not seem to correspond to periodic orbits which typically form f amilies in the polygonal boundary. The analysis using periodic-orbit q uantization and also Fourier transform of the density of states indeed yields evidence that there are certainly contributions from the corne r orbits which connect vertices of the boundary.