Classical and quantum-mechanical transition between regularity and irregularity in a Hamiltonian system

Abstract

We study the transition from regularity to irregularity for a physically real Hamiltonian system, viz., the hydrogen atom in a uniform magnetic field. We obtain quantitative correspondence between the transition in classical phase space and the change in the level statistics of the quantum energy spectra. Beyond the completely regular regime, the distributions of level spacings show a pronounced minimum at small spacings and cannot be accurately fitted by the semiclassical formula of Berry and Robnik [J. Phys. A 17, 2413 (1984)].