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Daily Overview |
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Pl 7: Plenary Lecture Location: Audimax A600 | |
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Mathematical models of quantum chaos University of Bristol, United Kingdom
I will report on recent progress towards fundamental conjectures in quantum chaos, which surmise that the statistics of quantum energy levels are governed by a Poisson point process if the system is completely integrable (Berry & Tabor, 1977) or by random matrix theory if the underlying classical dynamics is “chaotic” (Bohigas, Giannoni & Schmit, 1984). In the case of the Laplacian on flat tori, the question reduces to a natural problem on the distribution of values at integers of a quadratic form, which in turn is intimately related to the classical Oppenheim conjecture in number theory. We will also discuss the Laplacian on a compact hyperbolic surface and review some recent evidence for the emergence of random matrix statistics in the limit of high genus.
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