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The quasienergy spectrum of a periodically driven quantum system is constructed from classical dynamics by means of the semiclassical initial value representation using coherent states. For the first time, this method is applied to explicitly time dependent systems. For an anharmonic oscillator system with mixed chaotic and regular classical dynamics, the entire quantum spectrum (both regular and chaotic states) is reproduced semiclassically with surprising accuracy. In particular, the method is capable to account for the very small tunneling splittings.
Chaotic Billiards
(2000)
The frictionless motion of a particle on a plane billiard table The frictionless motion of a particle on a plane billiard table bounded by a closed curve provides a very simple example of a conservative classical system with non-trivial, chaotic dynamics. The limiting cases of strictly regular ("integrable") and strictly irregular ("ergodic") systems can be illustrated, as well as the typical case which shows an intricate mixture of regular and irregular behavior. Irregular orbits are characterized by an extremely sensitivity with respect to the initial conditions. Such billiard systems are exemplarily suited for educational purposes as models for simple systems with complicated dynamics as well as for far-reaching fundamental investigations.