Abstract
We investigate numerically the common α+β and the pure β FPU models, as well as some higher order generalizations. We consider initial conditions in which only low-frequency normal modes are excited, and perform a very accurate systematic study of the equilibrium time as a function of the number N of particles, the specific energy ε, and the parameters α and β. While at any fixed N the equilibrium time is found to be a stretched exponential in 1/ε, in the thermodynamic limit, i.e. for N→∞ at fixed ε, we observe a crossover to a power law. Concerning the (usually disregarded) dependence of T eq on α and β, we find it is nontrivial, and propose and test a general law. A central role is played by the comparison of the FPU models with the Toda model.
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Benettin, G., Ponno, A. Time-Scales to Equipartition in the Fermi–Pasta–Ulam Problem: Finite-Size Effects and Thermodynamic Limit. J Stat Phys 144, 793–812 (2011). https://doi.org/10.1007/s10955-011-0277-9
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DOI: https://doi.org/10.1007/s10955-011-0277-9