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

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

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 proceeding › Conference Contribution (Conference Proceeding)

5 Citations (Scopus)

Abstract

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 language	English
Title of host publication	Path Integrals - New Trends and Perspectives: Proc 9th Int Conf (Dresden)
Editors	W Janke, A Pelster
Publisher	World Scientific Publishing Co.
Publication status	Published - 2008

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title = "Near action-degenerate periodic-orbit bunches: a skeleton of chaos",

abstract = "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.",

author = "Alexander Altland and Petr Braun and Fritz Haake and Stefan Heusler and Gerhard Knieper and Sebastian Muller",

year = "2008",

language = "English",

editor = "W Janke and A Pelster",

booktitle = "Path Integrals - New Trends and Perspectives: Proc 9th Int Conf (Dresden)",

publisher = "World Scientific Publishing Co.",

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Near action-degenerate periodic-orbit bunches: a skeleton of chaos. / Altland, Alexander; Braun, Petr; Haake, Fritz et al.
Path Integrals - New Trends and Perspectives: Proc 9th Int Conf (Dresden). ed. / W Janke; A Pelster. World Scientific Publishing Co., 2008.

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

TY - GEN

T1 - Near action-degenerate periodic-orbit bunches: a skeleton of chaos

AU - Altland, Alexander

AU - Braun, Petr

AU - Haake, Fritz

AU - Heusler, Stefan

AU - Knieper, Gerhard

AU - Muller, Sebastian

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

M3 - Conference Contribution (Conference Proceeding)

BT - Path Integrals - New Trends and Perspectives: Proc 9th Int Conf (Dresden)

A2 - Janke, W

A2 - Pelster, A

PB - World Scientific Publishing Co.

ER -

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

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