1203.3587 (François Huveneers)

Thermal conductivity of weakly coupled integrable dynamics    [PDF]

François Huveneers

We study the Green-Kubo 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 $\epsilon >0$. In addition, the hamiltonian dynamics is perturbed by an energy preserving stochastic noise, which effect becomes only visible at very large time-scales, say $\epsilon^{-n}$ for some large fixed $n\ge 1$. We rigorously show that the conductivity $\kappa$ has a non-perturbative origin, meaning that $\kappa (\epsilon) = \mathcal O (\epsilon^{n+1})$. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz \cite{dha}, and to a classical spins chain recently investigated by Oganesyan, Pal and Huse \cite{oga}.

View original: http://arxiv.org/abs/1203.3587