Near action-degenerate periodic-orbit bunches: a skeleton of chaos

Alexander Altland, Petr Braun, Fritz Haake, Stefan Heusler, Gerhard Knieper, Sebastian Muller

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

5 Citations (Scopus)


Long periodic orbits of hyperbolic dynamics do not exist as independent individuals but rather come in closely packed bunches. Under weak resolution a bunch looks like a single orbit in configuration space, but close inspection reveals topological orbit-to-orbit differences. The construction principle of bunches involves close self-"encounters" of an orbit wherein two or more stretches stay close. A certain duality of encounters and the intervening "links" reveals an infinite hierarchical structure of orbit bunches. -- The orbit-to-orbit action differences ΔS within a bunch can be arbitrarily small. Bunches with ΔS of the order of Planck's constant have constructively interfering Feynman amplitudes for quantum observables, and this is why the classical bunching phenomenon could yield the semiclassical explanation of universal fluctuations in quantum spectra and transport.
Original languageEnglish
Title of host publicationPath Integrals - New Trends and Perspectives: Proc 9th Int Conf (Dresden)
EditorsW Janke, A Pelster
PublisherWorld Scientific Publishing Co.
Publication statusPublished - 2008


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