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.

Some analytic results on the FPU paradox / D. Bambusi, A. Carati, A. Maiocchi, A. Maspero (FIELDS INSTITUTE COMMUNICATIONS). - In: Hamiltonian partial differential equations and applications / [a cura di] P. Guyenne, D. Nicholls, C. Sulem. - New York : Springer, 2015. - ISBN 9781493929498. - pp. 235-254 [10.1007/978-1-4939-2950-4_8]

Some analytic results on the FPU paradox

D. Bambusi
;
A. Carati
Secondo
;
A. Maiocchi
Penultimo
;
A. Maspero
Ultimo
2015

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.
Mathematics (all)
Settore MAT/07 - Fisica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/354485
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