A review is given of the works on the FPU problem that were particularly relevant in connection with the metastability perspective, proposed in the year 1982. The idea is that there exists a specific energy threshold above which the time-averages of the relevant quantities quickly agree with the predictions of classical equilibrium statistical mechanics, whereas below it there exist two time scales. First there is a quick formation of a packet of low-frequency modes which do share the energy, and this produces a metastable state that lasts for a long time; then the system attains the final equilibrium state. There are strong indications that the specific energy threshold does not vanish in the limit of infinitely many particles. The review is given for the case of a one-dimensional FPU chain.

The Fermi-Pasta-Ulam problem and the metastability perspective / G. Benettin, A. Carati, L. Galgani, A. Giorgilli - In: The Fermi-Pasta-Ulam problem : a status report / [a cura di] G. Gallavotti. - Berlino : Springer, 2008. - ISBN 9783540729945. - pp. 151-189 (( convegno FPU 50 anni da FPU tenutosi a Roma nel 2004.

The Fermi-Pasta-Ulam problem and the metastability perspective

A. Carati
Secondo
;
L. Galgani
Penultimo
;
A. Giorgilli
Ultimo
2008

Abstract

A review is given of the works on the FPU problem that were particularly relevant in connection with the metastability perspective, proposed in the year 1982. The idea is that there exists a specific energy threshold above which the time-averages of the relevant quantities quickly agree with the predictions of classical equilibrium statistical mechanics, whereas below it there exist two time scales. First there is a quick formation of a packet of low-frequency modes which do share the energy, and this produces a metastable state that lasts for a long time; then the system attains the final equilibrium state. There are strong indications that the specific energy threshold does not vanish in the limit of infinitely many particles. The review is given for the case of a one-dimensional FPU chain.
Settore MAT/07 - Fisica Matematica
2008
Dipartimento di Fisica dell'Università "La Sapienza" di Roma
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/38527
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