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On the Energy Distribution in Fermi-Pasta-Ulam Lattices

Hairer, Ernst ; Lubich, Christian

In: Archive for Rational Mechanics and Analysis, 2012, vol. 205, no. 3, p. 993-1029

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    Titel
    • On the Energy Distribution in Fermi-Pasta-Ulam Lattices
    Autor
    • Hairer, Ernst. Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211, Geneva 4, Switzerland
    • Lubich, Christian. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle, 72076, Tübingen, Germany
    Dokumententyp
    • Postprint
    Sprache
    • Englisch
    Veröffentlicht in
    • Archive for Rational Mechanics and Analysis, 2012, vol. 205, no. 3, p. 993-1029. Springer-Verlag
    Andere elektronische Ausgabe
    Klassifikation
    • Mathematik
    OAI-PMH-ID
    • oai:doc.rero.ch:313668
    Summary
    This paper presents a rigorous study, for Fermi-Pasta-Ulam (FPU) chains with large particle numbers, of the formation of a packet of modes with geometrically decaying harmonic energies from an initially excited single low-frequency mode and the metastability of this packet over longer time scales. The analysis uses modulated Fourier expansions in time of solutions to the FPU system, and exploits the existence of almost-invariant energies in the modulation system. The results and techniques apply to the FPU α- and β-models as well as to higher-order nonlinearities. They are valid in the regime of scaling between particle number and total energy in which the FPU system can be viewed as a perturbation to a linear system, considered over time scales that go far beyond standard perturbation theory. Weak non-resonance estimates for the almost-resonant frequencies determine the time scales that can be covered by this analysis