Semiclassical spectra without periodic orbits for a kicked top.

Instytut Fizyki, Uniwersytet Jagielloński, ul. Reymonta 4, PL-30-059 Kraków, Poland (Received 24 June 1994) We present an h̄ ! 0 approximation for the quasienergy spectrum of a periodically kicked top, valid under conditions of both regular and chaotic classical motion. In contrast to conventional periodic-orbit theory we implement the semiclassical limit for each matrix element of the Floquet operator rather than for the trace of the propagator. Even though a classical looking action is involved, the approximate matrix elements are specified in terms of complex ghost trajectories instead of real classical orbits. Our mean error for the quasienergies is a surprisingly small 3% of the mean spacing.