2009/06/30 by Sebastian Müller, Stefan Heusler, Alexander Altland +2 · 2 citations
Physics and Astronomy · #cond-mat.mes-hall #nlin.CD
paper · pdf · doi:10.1088/1367-2630/11/10/103025
published as New J. Phys. 11, 103025 (2009) · 44 pages, 11 figures, changed title; final version published in New J. Phys. + additional appendices B-F not included in the journal version
arxiv created 2009/10/13 · arxiv updated 2009/12/01
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.