Quasi-harmonicity and power spectra in the FPU model

We evaluate the power spectra of the time series for the following simple o bservables in the Fermi-Pasta-Ulam model: harmonic energy kinetic energy, m icrocanonical density, Frenet-Serret curvature and the Lyapunov variable. F or some of these observables, also in the stochastic regime, the spectra sh ow a well defined quasi-harmonic structure, with harmonic frequencies shift ed with a single rescaling factor, as calculated in a previous paper. Even higher frequencies are excited: as replicas of the harmonic window at low e nergy, to end up with a smooth distribution at high energy, showing a power law behaviour (flicker noise). In the intermediate region the shape depend s on the observables, but in all cases the crossover is the maximum of the shifted harmonic spectrum. This establishes an intrinsic short-time scale d epending only on the energy density, as does the frequency rescaling factor For the curvature, we also evaluate the standard deviation: above threshol d, at increasing energy, it decreases exactly as the inverse of the rescali ng factor. This can be interpreted as a focalization around 'effective tori ' of a harmonic-like regime which apparently coexist with the chaotic motio n.