## Asymptotic localization of energy in non-disordered oscillator chains    [PDF]

Wojciech De Roeck, François Huveneers
We study two popular one-dimensional chains of classical anharmonic oscillators: the rotor chain and a version of the discrete non-linear Schr\"odinger chain. We assume that the interaction between neighboring oscillators, controlled by the parameter $\epsilon >0$, is small. We rigorously establish that the thermal conductivity of the chains has a non-perturbative origin, with respect to the coupling constant $\epsilon$, and we provide strong evidence that it decays faster than any power law in $\epsilon$ as $\epsilon \rightarrow 0$. The weak coupling regime also translates into a high temperature regime, suggesting that the conductivity vanishes faster than any power of the inverse temperature.
View original: http://arxiv.org/abs/1305.5127