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Theory of Dynamical Systems and the Relations Between Classical and Quantum Mechanics

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Abstract

We give a review of some works where it is shown that certain quantum-like features are exhibited by classical systems. Two kinds of problems are considered. The first one concerns the specific heat of crystals (the so called Fermi–Pasta–Ulam problem), where a glassy behavior is observed, and the energy distribution is found to be of Planck-like type. The second kind of problems concerns the self-interaction of a charged particle with the electromagnetic field, where an analog of the tunnel effect is proven to exist, and moreover some nonlocal effects are exhibited, leading to a natural hidden variable theory which violates Bell's inequalities.

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  1. Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133, Milano, Italy

    A. Carati & L. Galgani

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  1. A. Carati
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  2. L. Galgani
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Carati, A., Galgani, L. Theory of Dynamical Systems and the Relations Between Classical and Quantum Mechanics. Foundations of Physics 31, 69–87 (2001). https://doi.org/10.1023/A:1004103921290

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