Statistical Properties of Energy Levels in Non‐Born‐Oppenheimer Systems

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Abstract
Basic ideas and methods of the statistical analysis of energy spectra are reviewed. Complex nuclear, atomic and molecular spectra show typical fluctuation patterns which can be modeled with the aid of random matrices. Calculations on model systems and theoretical results show the existence of two universality classes of spectral fluctuations which depend on whether there are strong or only weak couplings between the various degrees of freedom. This correspondence also provides a link between quantum spectral statistics and classical dynamics. We illustrate statistical methods by analyzing model spectra obtained from a Hamiltonian which describes non‐Born‐Oppenheimer coupling of nuclear and electronic motion in molecules.