Some statistical properties of simple classically stochastic quantum systems

Abstract

Numerical studies are made of simple one- and two-dimensional quantum models which are stochastic in the classical limit. It is shown that the correlation properties of the quantum and corresponding classical motions are only similar for very short time intervals t s, and that the evolution of the quantum system, unlike the classical one, is stable. The diffusive excitation of the quantum system under a periodic perturbation is limited to a specific time interval t ∗ ≫ t s , during which the diffusion rate is similar to the corresponding classical diffusion rate. For the two-dimensional model, a continuous component in the correlation spectrum survives for an indefinite period t w ≫ t ∗ . It is shown that when the perturbation is quasiperiodic the interval t ∗ increases sharply.