Spectral properties of strongly perturbed Coulomb systems: Fluctuation properties

We study the fluctuation properties of large-scale quantum spectra of the hydrogen atom in a uniform magnetic field. The present data are of a statistical significance not reached by any other study of these topics. This allows us to tackle a number of problems, whose treatment has been prevented hitherto by the lack of sufficiently long spectral sequences. We mainly focus on the dependency of fluctuation properties on the parameter describing the classical transition from regularity to irregularity. Our results strongly indicate that there are no universal distributions for the nearest-neighbor spacings in the transition regime. Generally, fluctuation measures can show extraordinary behavior, which can be understood only by a detailed knowledge of the underlying classical dynamics rather than by a knowledge of the global classical phase-space structure.