APPLICATIONS OF CLASSICAL PERIODIC ORBIT THEORY TO CIRCULAR BILLIARDSWITH SMALL SCATTERING CENTERS

Mesoscopic systems like metallic clusters in three dimensions as well as quantum dots in two dimensions have raised a particular interest in the semiclassical interpretation of shell effects. We use periodic or bit theory to calculate the density of states for two-dimensional circ ular billiards. When a singular magnetic flux line is added at the cen ter of the disk, we show that the Aharonov-Bohm (AB) effect manifests itself through the cancellation of periodic orbits and the appearance of a new signal in the Fourier transform of the quantum density of sta tes. The same effects are also found analytically for a two-dimensiona l harmonic oscillator potential with flux line. Finally, we show that a homogeneous magnetic field B perpendicular to the disk plane leads t o B-periodic oscillations of the level density, which recently have al so been observed experimentally in two-dimensional circular quantum do ts.