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DY: Fachverband Dynamik und Statistische Physik

DY 20: Quantum chaos I

DY 20.1: Hauptvortrag

Mittwoch, 28. März 2007, 14:00–14:30, H2

Semiclassical approach to universality in quantum chaos — Stefan Heusler¹, •Sebastian Müller², Alexander Altland³, Petr Braun^1,4, and Fritz Haake¹ — ¹Fachbereich Physik, Universität Duisburg-Essen, 47048 Duisburg, Germany — ²Cavendish Laboratory, University of Cambridge, Cambridge CB30HE, UK — ³Institut für Theoretische Physik, Zülpicher Str 77, 50937 Köln, Germany — ⁴Institute of Physics, Saint-Petersburg University, 198504 Saint-Petersburg, Russia

According to the so-called Bohigas-Giannoni-Schmit conjecture the quantum spectra of classically chaotic systems display universal fluctuations. We explain this universality using periodic-orbit theory. To do so, we work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. We show that the interference between the contributions of these orbits gives rise to universal spectral correlations, agreeing with the predictions of random-matrix theory. In contrast to previous work the present approach yields both the non-oscillatory and the oscillatory parts of the universal spectral correlator. In particular, a semiclassical understanding of (the different possible degrees of) level repulsion is thus reached.

[1] S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake, nlin.CD/0610053, accepted for publication in Phys. Rev. Lett. (2007).