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

Huveneers, François

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

Type

Article accepté pour publication ou publié

Date

2013

Nom de la revue

Nonlinearity

Volume

Numéro

Éditeur

IOP Publishing

Résumé (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).

Mots-clés

Condensed matter: structural, mechanical & thermal; Statistical physics and nonlinear systems