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Some Analytic Results on the FPU Paradox

  • Dario BambusiEmail author
  • Andrea Carati
  • Alberto Maiocchi
  • Alberto Maspero
Chapter
Part of the Fields Institute Communications book series (FIC, volume 75)

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.

Keywords

Thermodynamic Limit Gibbs Measure Fourier Mode Toda Lattice Action Angle Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We thank Luigi Galgani for many interesting discussions and for his careful reading of the manuscript. This research was founded by the Prin project 2010–2011 “Teorie geometriche e analitiche dei sistemi Hamiltoniani in dimensioni finite e infinite”.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Dario Bambusi
    • 1
    Email author
  • Andrea Carati
    • 1
  • Alberto Maiocchi
    • 2
  • Alberto Maspero
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly
  2. 2.Laboratoire de MathématiquesUniversité de Cergy-PontoiseCergy-PontoiseFrance

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