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

Christodoulidi, Helen, Bountis, Tassos, Tsallis, Constantino and Drossos, Lambros (2016) Dynamics and statistics of the Fermi–Pasta–Ulam β-model with different ranges of particle interactions. Journal of Statistical Mechanics: Theory and Experiment, 2016 (12). p. 123206. ISSN 1742-5468

Full content URL: http://doi.org/10.1088/1742-5468/aa4f0e

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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 α_1 and α_2 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< α_2<1, we obtain extrapolated values for q>1, as N goes to infinity, 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 (q_E)-exponentials (with q_E>1) when the quartic-term interactions are long-ranged, otherwise we get the standard Boltzmann-Gibbs weight, with q=1. The values of q_E coincide, within small discrepancies, with the values of q obtained by the momentum distributions.

Keywords:nonlinear dynamics, metastable states, thermalization, numerical simulations
Subjects:G Mathematical and Computer Sciences > G121 Mechanics (Mathematical)
F Physical Sciences > F340 Mathematical & Theoretical Physics
G Mathematical and Computer Sciences > G120 Applied Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:37013
Deposited On:16 Sep 2019 10:00

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