Chaos in the Hamiltonian mean-field model (Articolo in rivista)

Type
Label
  • Chaos in the Hamiltonian mean-field model (Articolo in rivista) (literal)
Anno
  • 2011-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1103/PhysRevE.84.066211 (literal)
Alternative label
  • Francesco Ginelli (1,2); Kazumasa A. Takeuchi (3,4); Hugues Chaté (3); Antonio Politi (2,5,6); Alessandro Torcini (5,6,7) (2011)
    Chaos in the Hamiltonian mean-field model
    in Physical review. E, Statistical, nonlinear, and soft matter physics (Print); American Physical Society (APS), College Pk (Stati Uniti d'America)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Francesco Ginelli (1,2); Kazumasa A. Takeuchi (3,4); Hugues Chaté (3); Antonio Politi (2,5,6); Alessandro Torcini (5,6,7) (literal)
Pagina inizio
  • 06621 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://link.aps.org/doi/10.1103/PhysRevE.84.066211 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 84 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
  • 11 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 6 (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • 1 Istituto dei Sistemi Complessi, CNR, via dei Taurini 19, I-00185 Roma, Italy 2 Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom 3 Service de Physique de l'État Condensé, CEA-Saclay, F-91191 Gif-sur-Yvette, France 4 Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 5 Istituto dei Sistemi Complessi, CNR, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy 6 Centro Interdipartimentale per lo Studio delle Dinamiche Complesse, via Sansone 1, I-50019 Sesto Fiorentino, Italy 7 INFN Sez. Firenze, via Sansone 1, I-50019 Sesto Fiorentino, Italy (literal)
Titolo
  • Chaos in the Hamiltonian mean-field model (literal)
Abstract
  • We study the dynamical properties of the canonical ordered phase of the Hamiltonian mean-field (HMF) model, in which N particles, globally coupled via pairwise attractive interactions, form a rotating cluster. Using a combination of numerical and analytical arguments, we first show that the largest Lyapunov exponent remains strictly positive in the infinite-size limit, converging to its asymptotic value with 1/ln N corrections. We then elucidate the scaling laws ruling the behavior of this asymptotic value in the critical region separating the ordered, clustered phase and the disordered phase present at high-energy densities. We also show that the full spectrum of Lyapunov exponents consists of a bulk component converging to the (zero) value taken by a test oscillator forced by the mean field, plus subextensive bands of O(ln N) exponents taking finite values. We finally investigate the robustness of these results by studying a \"2D\" extension of the HMF model where each particle is endowed with 4 degrees of freedom, thus allowing the emergence of chaos at the level of a single particle. Altogether, these results illustrate the subtle effects of global (or long-range) coupling and the importance of the order in which the infinite-time and infinite-size limits are taken: For an infinite-size HMF system represented by the Vlasov equation, no chaos is present, while chaos exists and subsists for any finite system size. (literal)
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