Analysis of hydrogen Rydberg spectra in a uniform magnetic field: uncovering the transition from regularity to irregularity in a real quantum system

Abstract

Studies of the behaviour of quantum systems in a range of energy where their classical counterparts undergo transitions from regularity to irregularity, as manifested in phase space by the gradual destruction of invariant tori, to date have largely been confined to model Hamiltonian systems such as harmonic oscillators with cubic, quartic, or higher-degree polynomial corrections, or the stadium problem. We show that phenomena which have turned out characteristic of the onset of "quantum stochasticity" in these model systems can in fact be recovered in the quantal energy spectra of a "real" physical system, viz. spectra of hydrogen Rydberg atoms in strong magnetic fields. This implies that one has a simple prototype system at hand in which to study - not only in theory but also in experiment, quantitatively and in detail, and as a function of a continuously tunable external parameter - phenomena that are expected to be typical of the quantum properties of nonintegrable systems in general.