2013/05/22 by Wojciech De Roeck, François Huveneers, De Roeck, Wojciech +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1305.5127
v1 -> v2: minor corrections, references added. 33 pages, 1 figure. To appear in Comm. Pure Appl. Math
arxiv created 2014/11/20 · arxiv updated 2014/11/21
We study two popular one-dimensional chains of classical anharmonic oscillators: the rotor chain and a version of the discrete non-linear Schrödinger chain. We assume that the interaction between neighboring oscillators, controlled by the parameter ε>0, is small. We rigorously establish that the thermal conductivity of the chains has a non-perturbative origin, with respect to the coupling constant ε, and we provide strong evidence that it decays faster than any power law in ε as ε→ 0. The weak coupling regime also translates into a high temperature regime, suggesting that the conductivity vanishes faster than any power of the inverse temperature.