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

A.P. MAJTEY; L.G. MOYANO; C. TSALLIS

Trieste

Conferencia; School an Conference on Complex Systems and Nonextensive Statistical Mechanics; 2006

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, being r the distance between maps. We verify that the largest Lyapunov exponent lambda_M scales with N, yielding weak chaos in the thermodynamic limit (hence lambda_M goes to 0). In the short-range case, lambda_M 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 tc scales with N, where the exponent appears to be numerically consistent with the following behavior(see text for details). Overall, the occuppation of the phase space appears to be gradual and in stages. All these results exhibit major conjectures formulated within nonextensive statistical mechanics (NSM). Moreover, they exhibit strong similarity between the present discrete-time system, and the H-XY Hamiltonian ferromagnetic model, also studied in the frame of NSM.