Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

L. G. Moyano (), A. P. Majtey () and C. Tsallis ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 52, issue 4, 493-500

Abstract: We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r -α , being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ M scales as λ M ∝ N -κ(α) , where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ M →0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t c scales as t c ∝N β(α) , where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α> 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Keywords: 05.20.-y Classical statistical mechanics; 05.45.-a Nonlinear dynamics and chaos; 05.70.Ln Nonequilibrium and irreversible thermodynamics; 05.90.+m Other topics in statistical physics; thermodynamics; and nonlinear dynamical systems (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1140/epjb/e2006-00327-2

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