Periodic-Orbit Theory of Level Correlations

Details Periodic-Orbit Theory of Level Correlations Periodic-Orbit Theory of Level Correlations

2006-10-20

arxiv.org/abs/nlin/0610053v1

Phys. Rev. Lett. 98, 044103 (2007)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 1 figure (+ web-only appendix with 2 pages, 1 figure)

Scientific paper

10.1103/PhysRevLett.98.044103

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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