Periodic-Orbit Theory of Level Correlations

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.

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

References in corpus (3)

• Semiclassical Foundation of Universality in Quantum Chaos
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Semiclassical Theory of Chaotic Conductors

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• Bouncing ball orbits and symmetry breaking effects in a three-dimensional chaotic billiard
• Semiclassical spectral correlator in quasi one-dimensional systems