Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions
Huveneers, François (2013), Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions, Nonlinearity, 26, 3. http://dx.doi.org/10.1088/0951-7715/26/3/837
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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 → 0. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz (2008 Phys. Rev. Lett. 100 134301), and to a classic spin chain recently investigated by Oganesyan, Pal and Huse (2009 Phys. Rev. B 80 115104).
Subjects / KeywordsCondensed matter: structural, mechanical & thermal; Statistical physics and nonlinear systems
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