PMID: 22587080May 17, 2012Paper

Non-Maxwellian behavior and quasistationary regimes near the modal solutions of the Fermi-Pasta-Ulam β system

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
M LeoC Tsallis

Abstract

In a recent paper [M. Leo, R. A. Leo, and P. Tempesta, J. Stat. Mech. (2011) P03003], it has been shown that the π/2-mode exact nonlinear solution of the Fermi-Pasta-Ulam β system, with periodic boundary conditions, admits two energy density thresholds. For values of the energy density ε below or above these thresholds, the solution is stable. Between them, the behavior of the solution is unstable, first recurrent and then chaotic. In this paper, we study the chaotic behavior between the two thresholds from a statistical point of view, by analyzing the distribution function of a dynamical variable that is zero when the solution is stable and fluctuates around zero when it is unstable. For mesoscopic systems clear numerical evidence emerges that near the second threshold, in a large range of the energy density, the numerical distribution is fitted accurately with a q-Gaussian distribution for very large integration times, suggesting the existence of a quasistationary state possessing a weakly chaotic behavior. A normal distribution is recovered in the thermodynamic limit.

References

Sep 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M Antoni, S Ruffo
Jun 1, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A CafarellaR A Leo
Dec 13, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M Leo, R A Leo
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M Leo, R A Leo
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ozgur Afsar, Ugur Tirnakli
Sep 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Piergiulio Tempesta

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Citations

Jul 15, 2019·Entropy·Constantino Tsallis

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