Semiclassical Foundation of Universality in Quantum Chaos

Sebastian Müller, Stefan Heusler, Petr Braun, Fritz Haake, and Alexander Altland
Phys. Rev. Lett. 93, 014103 – Published 2 July 2004

Abstract

We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing. We show how in the semiclassical limit all system specific properties fade away, leaving only ergodicity, hyperbolicity, and combinatorics as agents determining the contributions of pairs of classical periodic orbits to the quantum spectral form factor. The small-time form factor is thus reproduced semiclassically. Bridges between classical orbits and (the nonlinear sigma model of) quantum field theory are built by revealing the contributing orbit pairs as topologically equivalent to Feynman diagrams.

  • Figure
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  • Received 15 January 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.014103

©2004 American Physical Society

Authors & Affiliations

Sebastian Müller1, Stefan Heusler1, Petr Braun1,2, Fritz Haake1, and Alexander Altland3

  • 1Fachbereich Physik, Universität Duisburg-Essen, 45117 Essen, Germany
  • 2Institute of Physics, Saint-Petersburg University, 198504 Saint-Petersburg, Russia
  • 3Institut für Theoretische Physik, Zülpicher Strasse 77, 50937 Köln, Germany

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Vol. 93, Iss. 1 — 2 July 2004

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