ABSTRACT
This chapter presents an investigation of the dynamics of one anisotropic spin in an external, periodically time-dependent field. The simple quantum system displays chaotic behavior in the classical limit. Chaotic behavior in classical deterministic systems is characterized by an extremely sensitive dependence on initial conditions. The statistics of quasienergy levels are discussed for our driven spin system with a twofold purpose. The statistics of quasienergy levels is equivalent to the energy level statistics in a time-independent system and the dependence of the quasienergy level statistics on the quantum parameter is investigated. The statistical properties of the spectrum of a quantum problem in its classical limit are associated with the regularity properties of the corresponding classical system. Using the complementary approaches of phase space analysis and level statistics we have shown in both schemes that for large spins, i.e. in the semiclassical regime, stochasticity can be discussed using concepts developed for classical systems.
