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We discover quantum Hall like jumps in the saturation spectral rigidity inthe semiclassical spectrum of a modified Kepler problem as a function of theinterval center. These jumps correspond to integer decreases of the radialwinding numbers in classical periodic motion. We also discover and explainsingle harmonic dominated oscillations of the level number variance with thewidth of the energy interval. The level number variance becomes effectivelyzero for the interval widths defined by the frequency of the shortest periodicorbit. This signifies that there are virtually no variations from sample tosample in the number of levels on such intervals.Comment: 18 pages, 3 color figures inlin

physical review. e, statistical, nonlinear and soft matter physics

Quantum jumps of saturation level rigidity and anomalous oscillations of level number variance in the semiclassical spectrum of a modified Kepler problem