Chaos induced by quantum effect due to breakdown of the Born-Oppenheimer adiabaticity

Abstract

Chaos in the multimode nonadiabatic system constructed by Heller [J. Chem. Phys. 92, 1718 (1990)], which consists of two diabatic two-dimensional harmonic potentials with the Condon coupling, is studied. A thorough investigation is carried out by scanning the magnitudes of the Condon coupling and the Duschinsky angle. To elucidate mechanisms that can cause chaos in this quantum system, the statistical properties of the energy levels and eigenfunctions of the system are investigated. We find an evidence in terms of the nearest-neighbor spacing distribution of energy levels and other measures that a certain class of chaos is purely induced by the nonadiabatic interaction due to breakdown of the Born-Oppenheimer approximation. Since the nonadiabatic transition can induce repeated bifurcation and merging of a wave packet around the region of quasicrossing between two potential surfaces, and since this interaction does not have a counterpart in the lower adiabatic system, the present chaos deserves being called "nonadiabatic chaos." Another type of chaos in a nonadiabatic system was previously identified [D. M. Leitner et al., J. Chem. Phys. 104, 434 (1996)] that reflects the inherent chaos of a corresponding adiabatic potential. We present a comparative study to establish the similarity and difference between these kinds of chaos.