Quantum Chaos in Generic Systems

Abstract

In this paper I offer an overview of the problem of energy level statistics in generic Hamiltonian systems, where classically we have regular motion on invariant tori for some initial conditions, and chaotic motion for some other complementary initial conditions. We look at this problem in the semiclassical limit of sufficiently small effective Planck's constant h_<eff>, assuming that we do have enough objects (asymptotically infinitely many) to define the statistics in this limit.