The Berry-Tabor Conjecture
One of the central observations ofquantum chaologyis that statistical properties of quantum spectra exhibit surprisingly universal features, which seem to mirror the chaotic or regular dynamical properties of the underlying classical limit. I will report on recent studies of simple regular systems, where some of the observed phenomena can be established rigorously. The results discussed are intimately related to the distribution of values of quadratic forms, and in particular to a quantitative version of the Oppenheim conjecture.
KeywordsPair Correlation Pair Correlation Function Geodesic Flow Quantitative Version Diophantine Condition
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