Regensburg 2007 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 20: Quantum chaos I
DY 20.1: Invited Talk
Wednesday, March 28, 2007, 14:00–14:30, H2
Semiclassical approach to universality in quantum chaos — Stefan Heusler1, •Sebastian Müller2, Alexander Altland3, Petr Braun1,4, 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).