Antonopoulous, Chris G. and Christodoulidi, Helen (2011) WEAK CHAOS DETECTION IN THE FERMI–PASTA–ULAM-α SYSTEM USING q-GAUSSIAN STATISTICS. International Journal of Bifurcation and Chaos, 21 (08). pp. 2285-2296. ISSN 0218-1274

Full content URL: http://doi.org/10.1142/S0218127411029781


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We study numerically statistical distributions of sums of orbit coordinates, viewed as independent random variables in the spirit of the Central Limit Theorem, in weakly chaotic regimes associated with the excitation of the first (k = 1) and last (k = N) linear normal modes of the Fermi–Pasta–Ulam-α system under fixed boundary conditions. We show that at low energies (E = 0.19), when k = 1 linear mode is excited, chaotic diffusion occurs characterized by distributions that are well approximated for long times (t > 10^9) by a q-Gaussian Quasi-Stationary State (QSS) with q ≈ 1.4. On the other hand, when k = N mode is excited at the same energy, diffusive phenomena are absent and the motion is quasi-periodic. In fact, as the energy increases to E = 0.3, the distributions in the former case pass through shorter q-Gaussian states and tend rapidly to a Gaussian (i.e. q → 1) where equipartition sets in, while in the latter we need to reach up to E = 4 to see a sudden transition to Gaussian statistics, without any passage through an intermediate QSS. This may be explained by different energy localization properties and recurrence phenomena in the two cases, supporting the view that when the energy is placed in the first mode weak chaos and "sticky" dynamics lead to a more gradual process of energy sharing, while strong chaos and equipartition appear abruptly when only the last mode is initially excited.

Keywords:Non-extensive statistical mechanics, q-Gaussian distributions, edge of chaos, quasi-stationary states
Subjects:F Physical Sciences > F340 Mathematical & Theoretical Physics
G Mathematical and Computer Sciences > G120 Applied Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:37111
Deposited On:16 Sep 2019 10:16

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