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Phys. Rev. Lett. 100, 184101 (2008) [4 pages]

Universality of Algebraic Decays in Hamiltonian Systems

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G. Cristadoro1,2 and R. Ketzmerick3,4
1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
2Center for Nonlinear and Complex Systems, Università degli Studi dell’Insubria, Via Valleggio 11, 22100 Como, Italy
3Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
4Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA

Received 17 January 2008; published 6 May 2008

Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincaré recurrences, with numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the existence of a universal asymptotic decay based on results for a Markov tree model with random scaling factors for the transition probabilities. Numerical simulations for different Hamiltonian systems support this conjecture and permit the determination of the universal exponent.

© 2008 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.100.184101
DOI:
10.1103/PhysRevLett.100.184101
PACS:
05.45.−a
 
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