Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

Abstract

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 $\epsilon \to 0$. 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.

21 pages

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• Glassy dynamics in strongly anharmonic chains of oscillators
• Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds