Macroscopic detection of the strong stochasticity threshold in Fermi-Pasta-Ulam chainsof 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 [Formula presented]. A crossover between weak and strong chaos is obtained at the same value [Formula presented] of the energy density [Formula presented] (energy per degree of freedom) for all the considered values of the impurity mass [Formula presented]. The threshold [Formula presented] coincides with the value of the energy density [Formula presented] 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 [M. Romero-Bastida and E. Braun, Phys. Rev. E 65, 036228 (2002)]. The complete Lyapunov spectrum does not depend significantly on the impurity mass [Formula presented]. 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 [Formula presented] of largest Lyapunov exponent. Implications of this result are discussed.