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Periodic-orbit theory of universal level repulsion | | Sebastian Müller
; Stefan Heusler
; Alexander Altland
; Petr Braun
; Fritz Haake
; | | Date: |
10 Jun 2009 | | Abstract: | 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. | | Source: | arXiv, 0906.1960 | | Services: | Forum | Review | PDF | Favorites | |
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