Periodic-orbit theory of universal level correlations in quantum chaos

S Muller, S Heusler, A Altland, P Braun, F Haake

Research output: Contribution to journalArticle (Academic Journal)peer-review

84 Citations (Scopus)


Using Gutzwiller's semiclassical periodic-orbit theory, we demonstrate universal behavior of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in establishing the full correlator such that its Fourier transform, the spectral form factor, is determined for all times, below and above the Heisenberg time. We cover dynamics with and without time-reversal invariance (from the orthogonal and unitary symmetry classes). A key step in our reasoning is to sum the periodic-orbit expansion in terms of a matrix integral, like the one known from the sigma model of random matrix theory.
Translated title of the contributionPeriodic-orbit theory of universal level correlations in quantum chaos
Original languageEnglish
Article number103025
Number of pages43
JournalNew Journal of Physics
Issue number10
Publication statusPublished - Oct 2009

Bibliographical note

Publisher: IOP


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