Nearly separable behavior of Fermi-Pasta-Ulam chains through the stochasticity threshold View Full Text


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Article Info

DATE

1995-04

AUTHORS

Carlo Alabiso, Mario Casartelli, Paolo Marenzoni

ABSTRACT

For the periodic Fermi-Pasta-Ulam chain with quartic potential we prove the relation 〈pk2〉T≈ (1+α) 〈ωk2qk2〉τ , i.e., the proportionality, already at early timesT, between averaged kinetic and harmonic energies of each mode. The factor α depends on the parameters of the model, but not on the mode and the number of degrees of freedom. It grows with the anharmonic strength from the value α=0 of the harmonic limit (virial theorem) up to few units for the system much above the threshold. In the stochastic regime the time necessary to reduce the fluctuations ink to a fixed percentage remains at least one order of magnitude smaller than the time necessary to reach a similar level of equipartition. The persistence of such a behavior even above the stochasticity threshold clarifies a number of previous numerical results on the relaxation to equilibrium: e.g., the existence of several time scales and the relevance of the harmonic frequency spectrum. The difficulties in the numerical simulation of the thermodynamic limit are also discussed. More... »

PAGES

451-471

References to SciGraph publications

  • 1987-02. Complexity, rate of energy exchanges and stochasticity in IL NUOVO CIMENTO B (1971-1996)
  • 1994-07. Equipartition thresholds in chains of anharmonic oscillators in JOURNAL OF STATISTICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/bf02179398

    DOI

    http://dx.doi.org/10.1007/bf02179398

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