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

摘要

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(-alpha), being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0 +/- 1, and short-range (integrable) when alpha > 1. We verify that the largest Lyapunov exponent lambda(M) scales as lambda(M) proportional to N-kappa(alpha), where kappa(alpha) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N -> infinity (hence lambda(M) -> 0). In the short-range case, kappa(alpha) 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) proportional to N-beta(alpha), where beta(alpha) appears to be numerically in agreement with the following behavior: beta > 0 for 0 = 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 alpha-XY Hamiltonian ferromagnetic model.