Dynamics and statistics of the Fermi-Pasta-Ulam β-model with different ranges of particle interactions

Helen Christodoulidi, Tassos Bountis, Constantino Tsallis, Lambros Drossos

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


In the present work we study the Fermi-Pasta-Ulam (FPU) β-model involving long-range interactions (LRI) in both the quadratic and quartic potentials, by introducing two independent exponents α1 and α2 respectively, which make the forces decay with distance r. Our results demonstrate that weak chaos, in the sense of decreasing Lyapunov exponents, and q-Gaussian probability density functions (pdfs) of sums of the momenta, occurs only when long-range interactions are included in the quartic part. More importantly, for 0 ≤ α2<1, we obtain extrapolated values for q≡q∞<1, as N→∞, suggesting that these pdfs persist in that limit. On the other hand, when long-range interactions are imposed only on the quadratic part, strong chaos and purely Gaussian pdfs are always obtained for the momenta. We have also focused on similar pdfs for the particle energies and have obtained qE-exponentials (with qE < 1) when the quartic-term interactions are long-ranged, otherwise we get the standard Boltzmann-Gibbs weight, with q = 1. The values of qE coincide, within small discrepancies, with the values of q obtained by the momentum distributions.

Original languageEnglish
Article number123206
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number12
Publication statusPublished - Dec 22 2016
Externally publishedYes


  • metastable states
  • nonlinear dynamics
  • numerical simulations
  • thermalization

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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