Semiclassical foundation of universality in quantum chaos

S Muller, S Heusler, P Braun, F Haake, A Altland

Research output: Contribution to journalArticle (Academic Journal)peer-review

183 Citations (Scopus)


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.
Translated title of the contributionSemiclassical foundation of universality in quantum chaos
Original languageEnglish
Article numberArticle no. 014103
Pages (from-to)1 - 4
Number of pages4
JournalPhysical Review Letters
Volume93 (1)
Publication statusPublished - Jul 2004

Bibliographical note

Publisher: American Physical Soc


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