Thermal conductivity of disordered lattices in the weak coupling regime

Details Thermal conductivity of disordered lattices in the weak coupling regime Thermal conductivity of disordered lattices in the weak coupling regime

2012-03-15

arxiv.org/abs/1203.3587v3

Physics

Condensed Matter

Statistical Mechanics

20 pages, weak coupling added

Scientific paper

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.

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