Thermal conductivity of disordered lattices in the weak coupling regime
Huveneers, François (2012), Thermal conductivity of disordered lattices in the weak coupling regime. https://basepub.dauphine.fr/handle/123456789/9428
TypeDocument de travail / Working paper
Series titleUniversité Paris-Dauphine
MetadataShow full item record
Abstract (EN)We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter $\epsilon > 0$. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in $\epsilon$ as $\epsilon\rightarrow 0$. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz, and to a classical spins chain recently investigated by Oganesyan, Pal and Huse.
Subjects / KeywordsWeak interactions (Nuclear physics); Heat -- Transmission
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