Classical-Quantum Correspondence in the Presence of Global Chaos

Abstract

We compare the classical and quantum mechanics of a system whose classical dynamics are dominated by chaos. We observe a quantum "scars" of short periodic orbits. By examining the states on a quantum surface of section, we find that the stable and unstable manifolds of the periodic orbits have a clear effect on the eigenstates, in addition to the orbits themselves. A local density operator, constructed from a band of energy eigenstates, is strongly scarred by short periodic orbits. We also demonstrate a relation between the quantum eigenvalue spectrum and the actions of the periodic orbits.