In this paper we report and discuss some recent results obtained investigating with numerical methods the celebrated Fermi--Pasta--Ulam model, a chain of non--linearly coupled oscillators with identical masses. We are interested in the evolution towards equipartition when energy is initially given to one or a few modes. Using the spectral entropy as a numerical indicator there is a strong suggestion that the relaxation time to equipartition increases exponentially with an inverse power of the specific energy. Such a scaling appears to remain valid in the thermodynamic limit.
Relaxation times to equilibrium in Fermi-Pasta-Ulam system / S. Paleari, T. Penati - In: SYMMETRY AND PERTURBATION THEORY Proceedings of the International Conference on SPT2004 / Giuseppe Gaeta, Barbari Prinari, Stefan Rauch-Wojciechowski, Susanna Terracini. - Singapore : World Scientific Publishing, 2005. - ISBN 981-256-136-6. - pp. 255-263 (( convegno Symmetry and Perturbation Theory tenutosi a Cala Gonone, Sardinia, Italy nel 2004.
Relaxation times to equilibrium in Fermi-Pasta-Ulam system
S. PaleariPrimo
;T. PenatiUltimo
2005
Abstract
In this paper we report and discuss some recent results obtained investigating with numerical methods the celebrated Fermi--Pasta--Ulam model, a chain of non--linearly coupled oscillators with identical masses. We are interested in the evolution towards equipartition when energy is initially given to one or a few modes. Using the spectral entropy as a numerical indicator there is a strong suggestion that the relaxation time to equipartition increases exponentially with an inverse power of the specific energy. Such a scaling appears to remain valid in the thermodynamic limit.
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