Asymptotic localization of energy in non-disordered oscillator chains
Huveneers, François; De Roeck, Wojciech (2015), Asymptotic localization of energy in non-disordered oscillator chains, Communications on Pure and Applied Mathematics, 68, 9. http://dx.doi.org/10.1002/cpa.21550
TypeArticle accepté pour publication ou publié
External document linkhttp://fr.arxiv.org/abs/1305.5127
Journal nameCommunications on Pure and Applied Mathematics
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Abstract (EN)We study two popular one-dimensional chains of classical anharmonic oscillators: the rotor chain and a version of the discrete non-linear Schrödinger 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.
Subjects / Keywordsthermal conductivity; non-linear Schrödinger chain; oscillator chains
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