Abstract
We study two popular one‐dimensional chains of classical anharmonic oscillators: the rotor chain and a version of the discrete nonlinear Schrödinger chain. We assume that the interaction between neighboring oscillators, controlled by the parameter ɛ > 0, is small. We rigorously establish that the thermal conductivity of the chains has a nonperturbative origin with respect to the coupling constant ɛ, and we provide strong evidence that it decays faster than any power law in ɛ as ɛ → 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. To our knowledge, it is the first time that a clear connection has been established between KAM‐like phenomena and thermal conductivity. © 2015 Wiley Periodicals, Inc.
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