Periodic-orbit theory of universal level correlations in quantum chaos

Details Periodic-orbit theory of universal level correlations in quantum chaos Periodic-orbit theory of universal level correlations in quantum chaos

2009-06-10

arxiv.org/abs/0906.1960v2

New J. Phys. 11, 103025 (2009)

Nonlinear Sciences

Chaotic Dynamics

44 pages, 11 figures, changed title; final version published in New J. Phys. + additional appendices B-F not included in the j

Scientific paper

10.1088/1367-2630/11/10/103025

Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour 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.

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