Macroscopic detection of the strong stochasticity threshold in Fermi-Pasta-Ulam chains of oscillators.
The largest Lyapunov exponent of a system composed by a heavy impurity embedded in a chain of anharmonic nearest-neighbor Fermi-Pasta-Ulam oscillators is numerically computed for various values of the impurity mass M. A crossover between weak and strong chaos is obtained at the same value epsilon(T) of the energy density epsilon (energy per degree of freedom) for all the considered values of the impurity mass M. The threshold epsilon(T) coincides with the value of the energy density epsilon at which a change of scaling of the relaxation time of the momentum autocorrelation function of the impurity occurs and that was obtained in a previous work [Phys. Rev. E 65, 036228 (2002)]]. The complete Lyapunov spectrum does not depend significantly on the impurity mass M. These results suggest that the impurity does not contribute significantly to the dynamical instability (chaos) of the chain and can be considered as a probe for the dynamics of the system to which the impurity is coupled. Finally, it is shown that the Kolmogorov-Sinai entropy of the chain has a crossover from weak to strong chaos at the same value of the energy density as the crossover value epsilon(T) of largest Lyapunov exponent. Implications of this result are discussed.
Romero-Bastida
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Departmento de Física, Universidad Autónoma Metropolitana Iztapalapa, Apartado Postal 55-534, Distrito Federal 09340, Mexico. rbm@xanum.uam.mx