document: Quantum sensitive dependence Wave functions of bounded quantum systems with time-independent potentials , being almost periodic functions , can not 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
doc_bio_tags: B I I B I O B I I O O O O O O B I O O O O B I O O B I O O O B I I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O B I I O O O O O O O O B I I O O O O O O O O O
extractive_keyphrases: quantum sensitive dependence wave functions bounded quantum systems periodic functions time asymptotics classical chaos quantum control classical lyapunov exponent operator matrix elements
abstractive_keyphrases: time-independent potentials time-dependent interactions quantum complexity