Sebastian Müller et al 2009 New J. Phys. 11 103025 doi:10.1088/1367-2630/11/10/103025
Periodic-orbit theory of universal level correlations in quantum chaos
Sebastian Müller1, Stefan Heusler2, Alexander Altland3, Petr Braun4,5 and Fritz Haake4
Show affiliationsUsing 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.
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Issue 10 (October 2009)
Received 3 June 2009
Published 12 October 2009
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Periodic-orbit theory of universal level correlations in quantum chaos
Sebastian Müller et al 2009 New J. Phys. 11 103025
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