Generalized Floquet Operator for Quasiperiodically Driven Quantum Systems

Abstract

The behaviour of systems with time dependent perturbations can be qualitatively different from the one of isolated quantum systems, e.g. in a bounded spatial domain, or confined by a potential going rapidly to infinity. Since the energy levels of such a system are discrete, the wave function and thus all expectation values and correlation functions will of necessity be almost period in time [1]. This rules out any good ergodic properties or other forms of classical chaoticity, which require decay of correlation functions. Of course as the size of the system becomes large and the spacing between levels becomes very small, the ensemble averages of same classes of quantum variables may exhibit good decay properties over long time periods. These can become, in suitable limits, indistinguishable from those given by chaotic dynamics.