QUANTUM CHAOS - A DECOHERENT DEFINITION

We show that the rate of increase of Von Neumann entropy computed from the reduced density matrix of an open quantum system is an excellent indicator of the dynamical behavior of its classical Hamiltonian count erpart. In decohering quantum analogs of systems which exhibit classic al Hamiltonian chaos entropy production rate quickly tends to a consta nt which is given by the sum of the positive Lyapunov exponents, and f alls off only as the system approaches equilibrium, By contrast, integ rable systems tend to have an entropy production rate which decreases as t(-1) well before equilibrium is attained. Thus, behavior of quantu m systems in contact with the environment can be used as a test to det ermine the nature of their Hamiltonian evolution.