The measure of chaoticity in stationary quantum systems

Abstract

Our earlier suggested quantum chaoticity measure characterizing the initial symmetry breaking and the destruction of the corresponding integrals of motion in a perturbed system is used for the analysis of the quantum Henon-Heiles Hamiltonian and diamagnetic Kepler problem. We demonstrate that the critical perturbation parameter for the transition from regularity to chaos in the quantum systems is in remarkable agreement with the classical picture of chaotization. We also show that this critical parameter can be estimated in the framework of first-order perturbation theory.