Quantum dynamics of a nonintegrable system

Abstract

The quantum motion of a periodically kicked rotator is shown to be related to Anderson's problem of motion of a quantum particle in a one-dimensional lattice in the presence of a static-random potential. Classically, the first problem is nonintegrable and, for certain values of the parameters, exhibits chaos and diffusion in phase space; in the second problem, diffusion takes place in configuration space. Quantum phase interference, however, is known to suppress diffusion in Anderson's problem and to produce quasiperiodic motion. By establishing a mapping between the two systems we show that a similar effect determines the dynamics of the quantum rotator. As a result its wave functions are localized in phase space and their time evolution is quasiperiodic. This result explains the quantum recurrences and boundedness of the energy found in recent numerical work.