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Semiclassical Foundation of Universality in Quantum Chaos

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arxiv nlin/0401021 v2 pith:2HQCBGYM submitted 2004-01-15 nlin.CD cond-mat.mes-hall

Sebastian Müller , Stefan Heusler , Petr Braun , Fritz Haake , Alexander Altland This is my paper · ORCID
classification nlin.CDcond-mat.mes-hall
keywords quantumclassicalsemiclassicalchaosfactorformorbitspairs
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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 non-linear sigma model of) quantum field theory are built by revealing the contributing orbit pairs as topologically equivalent to Feynman diagrams.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Controlled Chaos in 4D SCFTs

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    Orbifolds of N=4 SYM produce SCFTs whose dilatation operator in a subsector is realized by a tunable spin chain whose eigenvalue statistics exhibit chaos for specific marginal couplings.

  2. Krylov Complexity in Mixed Phase Space

    hep-th 2024-12 conditional novelty 6.0 of 10

    The Krylov complexity peak height correlates with the Brody parameter in mixed-phase-space quantum systems, diminishing as the spectrum becomes Poissonian.

  3. Chaotic-Integrable Transition for Disordered Orbital Hatsugai-Kohmoto Model

    cond-mat.str-el 2024-11 conditional novelty 5.0 of 10

    Disordered orbital Hatsugai-Kohmoto model shows a transition from Poisson to GOE level statistics as interaction disorder increases, while OTOC plateau values fail to uniformly distinguish chaos across models.

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