Quantum ergodicity of a coherence-preserving SU(2) Hamiltonian system with quasiperiodic kicking.

Abstract

In this paper we study the time evolution of a quasiperiodically kicked spin system whose Hamiltonian is linear in the SU(2) generators. Since this Hamiltonian preserves SU(2) coherent states under time evolution, there is a close correspondence between the quantum evolution and the classical evolution of the system on the Bloch sphere. Such a system has previously been studied by Milonni, Ackerhalt, and Goggin [Phys. Rev. A 35, 1714 (1987)] and, with two incommensurate driving frequencies, the quantum evolution was characterized by (a) decay of the autocorrelation function of the state vector, (b) broadband power spectrum of observables, (c) ergodicity on the Bloch sphere. We expand upon their work to study the corresponding behavior of the motion on a symplectic phase space and the decay of the autocorrelation function of the state vector. When the forcing strength is such that the motion is localized in phase space, the autocorrelation function shows revivals. When the motion is ergodic the autocorrelation function rapidly decays without revivals. The classical motion however is not chaotic, there is no sensitive dependence on initial conditions. For three incommensurate frequencies, the motion is more delocalized than for two frequencies for a fixed forcing strength.