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Regular and Chaotic Dynamics

, Volume 23, Issue 6, pp 704–719 | Cite as

The FPU Problem as a Statistical-mechanical Counterpart of the KAM Problem, and Its Relevance for the Foundations of Physics

  • Andrea CaratiEmail author
  • Luigi Galgani
  • Alberto Maiocchi
  • Fabrizio Gangemi
  • Roberto Gangemi
Article
  • 39 Downloads

Abstract

We give a review of the Fermi–Pasta–Ulam (FPU) problem from the perspective of its possible impact on the foundations of physics, concerning the relations between classical and quantum mechanics. In the first part we point out that the problem should be looked upon in a wide sense (whether the equilibrium Gibbs measure is attained) rather than in the original restricted sense (whether energy equipartition is attained). The second part is devoted to some very recent results of ours for an FPU-like model of an ionic crystal, which has such a realistic character as to reproduce in an impressively good way the experimental infrared spectra. Since the existence of sharp spectral lines is usually considered to be a characteristic quantum phenomenon, even unconceivable in a classical frame, this fact seems to support a thesis suggested by the original FPU result. Namely, that the relations between classical and quantum mechanics are much subtler than usually believed, and should perhaps be reconsidered under some new light.

Keywords

FPU problem foundations of statistical mechanics relations between classical and quantum physics 

MSC2010 numbers

82C03 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • Andrea Carati
    • 1
    Email author
  • Luigi Galgani
    • 1
  • Alberto Maiocchi
    • 1
  • Fabrizio Gangemi
    • 2
  • Roberto Gangemi
    • 2
  1. 1.Department of MathematicsUniversità degli Studi di MilanoMilanoItaly
  2. 2.DMMTUniversità di BresciaBresciaItaly

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