Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model

We present a numerical study of dynamical correlations (structure factors) of the long-range generalization of the Fermi-Pasta-Ulam oscillator chain, where the strength of the interaction between two lattice sites decays as a power alpha of the inverse of their distance. The structure factors at finite energy density display distinct peaks, corresponding to long-wavelength propagating modes, whose dispersion relation is compatible with the predictions of the linear theory. We demonstrate that dynamical scaling holds, with a dynamical exponent z that depends weakly on a in the range 1 < alpha < 3. The lineshapes have a non-trivial functional form and appear somehow independent of alpha. Within the accessible time and size ranges, we also find that the short-range limit is hardly attained even for relatively large values of alpha.