An Averaging Theorem for FPU in the Thermodynamic Limit View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2014-04

AUTHORS

A. Maiocchi, D. Bambusi, A. Carati

ABSTRACT

Consider an FPU chain composed of N≫1 particles, and endow the phase space with the Gibbs measure corresponding to a small temperature β-1. Given a fixed K, we construct K packets of normal modes whose energies are adiabatic invariants (i.e., are approximately constant for times of order β1-a, a>0) for initial data in a set of large measure. Furthermore, the time autocorrelation function of the energy of each packet does not decay significantly for times of order β. The restrictions on the shape of the packets are very mild. All estimates are uniform in the number N of particles and thus hold in the thermodynamic limit N→∞, β>0. More... »

PAGES

300-322

References to SciGraph publications

  • 2015-04. An Extensive Adiabatic Invariant for the Klein–Gordon Model in the Thermodynamic Limit in ANNALES HENRI POINCARÉ
  • 2013-07. The Fermi-Pasta-Ulam Problem and Its Underlying Integrable Dynamics in JOURNAL OF STATISTICAL PHYSICS
  • 2012-09. Extensive Adiabatic Invariants for Nonlinear Chains in JOURNAL OF STATISTICAL PHYSICS
  • 2013-02. Asymptotic Stability of N-Solitary Waves of the FPU Lattices in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2007-08. An Averaging Theorem for Hamiltonian Dynamical Systems in the Thermodynamic Limit in JOURNAL OF STATISTICAL PHYSICS
  • 1999. Scaling Limits of Interacting Particle Systems in NONE
  • 2008. The Fermi-Pasta-Ulam Problem, A Status Report in NONE
  • 2012-09. A Series Expansion for the Time Autocorrelation of Dynamical Variables in JOURNAL OF STATISTICAL PHYSICS
  • 2012-08. Exponentially Long Stability Times for a Nonlinear Lattice in the Thermodynamic Limit in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1978-04. Formal integrals for an autonomous Hamiltonian system near an equilibrium point in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2006-06. On Metastability in FPU in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2009-05. Asymptotic Stability of Lattice Solitons in the Energy Space in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10955-014-0958-2

    DOI

    http://dx.doi.org/10.1007/s10955-014-0958-2

    DIMENSIONS

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