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

*2018, Volume 23, Number 6, pp. 704-719*

Author(s):

**Carati A., Galgani L., Maiocchi A., Gangemi F., Gangemi R.**

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.

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