2014/05/14 by Helen Christodoulidi, Constantino Tsallis, Tassos Bountis · 1 citation
Physics and Astronomy · #cond-mat.stat-mech #nlin.CD
paper · pdf · doi:10.1209/0295-5075/108/40006
8 pages, 5 fugures
arxiv created 2014/05/14 · arxiv updated 2015/06/19
We introduce and numerically study a long-range-interaction generalization of the one-dimensional Fermi-Pasta-Ulam (FPU) β- model. The standard quartic interaction is generalized through a coupling constant that decays as 1/rα (α≥ 0)(with strength characterized by b>0). In the α→∞ limit we recover the original FPU model. Through classical molecular dynamics computations we show that (i) For α≥ 1 the maximal Lyapunov exponent remains finite and positive for increasing number of oscillators N (thus yielding ergodicity), whereas, for 0 ≤ α<1, it asymptotically decreases as N- κ(α) (consistent with violation of ergodicity); (ii) The distribution of time-averaged velocities is Maxwellian for α large enough, whereas it is well approached by a q-Gaussian, with the index q(α) monotonically decreasing from about 1.5 to 1 (Gaussian) when α increases from zero to close to one. For α small enough, the whole picture is consistent with a crossover at time tc from q-statistics to Boltzmann-Gibbs (BG) thermostatistics. More precisely, we construct a "phase diagram" for the system in which this crossover occurs through a frontier of the form 1/N ∝ bδ/tcγ with γ>0 and δ>0, in such a way that the q=1 (q>1) behavior dominates in the limN →∞ limt →∞ ordering (limt →∞ limN →∞ ordering).