The notion of persistence applied to breathers in thermal equilibrium

We study the thermal equilibrium of nonlinear Klein-Gordon chains at the limit of small coupling (an-ticontinuum limit). We show that the persistence distribution associated to the local energy density is a useful tool to study the statistical distribution of so-called thermal breathers, mainly when the equilibrium is characterized by long-lived static excitations; in that case, the distribution of persistence intervals turns out to be a powerlaw. We demonstrate also that this generic behaviour has a counterpart in the power spectra, where the high frequencies domains nicely collapse if properly rescaled. These results are also compared to non linear Klein-Gordon chains with a soft nonlinearity, for which the thermal breathers are rather mobile entities. Finally, we discuss the possibility of a breather-induced anomalous diffusion law, and show that despite a strong slowing-down of the energy diffusion, there are numerical evidences for a normal asymptotic diffusion mechanism, but with exceptionnally small diffusion coefficients.