QUANTUM EFFECTS OF PERIODIC-ORBITS FOR THE KICKED TOP

We analyze traces of powers of the time evolution operator of a period ically kicked top. Semiclassically, such traces are related to periodi c orbits of the classical map. We derive the semiclassical traces in a coherent state basis and show how the periodic orbits can be recovere d via a Fourier transform. A breakdown of the stationary phase approxi mation is detected. The quasi energy spectrum remains elusive due to l ack of knowledge of sufficiently many periodic orbits. Divergencies of periodic orbit formulas are avoided by appealing to the finiteness of the quantum mechanical Hilbert space. The traces also enter the coeff icients of the characteristic polynominal of the Floquet operator. Sta tistical properties of these coefficients give rise to a new criterion for the distinction of chaos and regular motion.