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

LUIS G. MOYANO; ANA P. MAJTEY; CONSTANTINO TSALLIS

EUROPEAN PHYSICAL JOURNAL B - CONDENSED MATTER

SPRINGER

Lugar: Heidelberg; Año: 2006 vol. 52 p. 493 - 493

1434-6028

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\leq alpha \leq 1, and short-range (integrable) when alpha >1. We verify that the largest Lyapunov exponent lambda_M scales as lambda_M \sim N^kappa(alpha), where kappa(alpha) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N\rightarrow\infty hence lambda_M\rightarrow\infty). 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 \simN^beta(alpha), where beta(alpha) appears to be numerically in agreement with the following behavior: \beta>0 for 0 \leq alpha < 1, and zero for alpha \geq 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.