TIME EVOLUTION OF CHAOTIC QUANTUM-SYSTEMS

We consider a quantum system which is open in the sense that a number of metastable states are coupled to a set of decay channels. A solution of the time dependent Schrödinger equation is developed that allows us to describe both the excitation and the decay process. Assuming the excitation to be practically instantaneous, the decay is studied in detail for systems which have a random Hamiltonian or-what is closely related-behave chaotically. The decay function is worked out in a form amenable to numerical evaluation with standard techniques. For several instructive special cases, it is evaluated in closed analytical form. It turns out to be generally neither exponential nor independent of the way by which the system was excited. It is exponential and independent of the excitation only if a large number of decay channels are present. If only one channel is open, the decay function is asymptotically proportional to t-3/2. © 1992 Academic Press, Inc.