Quantum sensitive dependence

Abstract

Wave functions of bounded quantum systems with time-independent potentials, being almost periodic functions, cannot have time asymptotics as in classical chaos. However, bounded quantum systems with time-dependent interactions, as used in quantum control, may have continuous spectrum and the rate of growth of observables is an issue of both theoretical and practical concern. Rates of growth in quantum mechanics are discussed by constructing quantities with the same physical meaning as those involved in the classical Lyapunov exponent. A generalized notion of quantum sensitive dependence is introduced and the mathematical structure of the operator matrix elements that correspond to different types of growth is characterized.