Some Analytic Results on the FPU Paradox View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2015

AUTHORS

Dario Bambusi , Andrea Carati , Alberto Maiocchi , Alberto Maspero

ABSTRACT

We present some analytic results aiming at explaining the lack of thermalization observed by Fermi Pasta and Ulam in their celebrated numerical experiment. In particular we focus on results which persist as the number N of particles tends to infinity. After recalling the FPU experiment and some classical heuristic ideas that have been used for its explanation, we concentrate on more recent rigorous results which are based on the use of (i) canonical perturbation theory and KdV equation, (ii) Toda lattice, (iii) a new approach based on the construction of functions which are adiabatic invariants with large probability in the Gibbs measure. More... »

PAGES

235-254

References to SciGraph publications

  • 2001-05. Symmetry and Resonance in Periodic FPU Chains in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1978-04. Formal integrals for an autonomous Hamiltonian system near an equilibrium point in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2011-02. Hill’s potentials in weighted Sobolev spaces and their spectral gaps in MATHEMATISCHE ANNALEN
  • 2012-09. On the Energy Distribution in Fermi–Pasta–Ulam Lattices in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2013-07. The Fermi-Pasta-Ulam Problem and Its Underlying Integrable Dynamics in JOURNAL OF STATISTICAL PHYSICS
  • 1985-10. Numerical investigations on a chain of weakly coupled rotators in the light of classical perturbation theory in IL NUOVO CIMENTO B (1971-1996)
  • 2014-04. An Averaging Theorem for FPU in the Thermodynamic Limit in JOURNAL OF STATISTICAL PHYSICS
  • 2005. The Fermi-Pasta-Ulam Problem in the Thermodynamic Limit in CHAOTIC DYNAMICS AND TRANSPORT IN CLASSICAL AND QUANTUM SYSTEMS
  • 2011-08. Time-Scales to Equipartition in the Fermi–Pasta–Ulam Problem: Finite-Size Effects and Thermodynamic Limit in JOURNAL OF STATISTICAL PHYSICS
  • 2007-08. An Averaging Theorem for Hamiltonian Dynamical Systems in the Thermodynamic Limit in JOURNAL OF STATISTICAL PHYSICS
  • 1989-12. Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1985-10. Classical perturbation theory for systems of weakly coupled rotators in IL NUOVO CIMENTO B (1971-1996)
  • 1987-03. Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part I in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2012-08. Exponentially Long Stability Times for a Nonlinear Lattice in the Thermodynamic Limit in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1993-05. Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems in JOURNAL OF STATISTICAL PHYSICS
  • 2006-06. On Metastability in FPU in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Book

    TITLE

    Hamiltonian Partial Differential Equations and Applications

    ISBN

    978-1-4939-2949-8
    978-1-4939-2950-4

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-1-4939-2950-4_8

    DOI

    http://dx.doi.org/10.1007/978-1-4939-2950-4_8

    DIMENSIONS

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