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Periodic-Orbit Theory of Level Correlations

Stefan Heusler·Sebastian Müller·Alexander Altland·Petr Braun·Fritz Haake
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Abstract

We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the non-oscillatory and the oscillatory part of the universal spectral correlator are obtained. Borel summation of the series reproduces the exact correlator of random-matrix theory.

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Stefan Heusler, Sebastian Müller, Alexander Altland, Petr Braun, Fritz Haake. 2006-10-20. Periodic-Orbit Theory of Level Correlations. https://doi.org/10.1103/physrevlett.98.044103

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