Author:

Keywords:

Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, THERMAL-CONDUCTIVITY, SYSTEMS, THEOREM, cond-mat.stat-mech, math-ph, math.MP, 0101 Pure Mathematics, 0102 Applied Mathematics, General Mathematics, 4901 Applied mathematics, 4904 Pure mathematics

Abstract:

© 2015 Wiley Periodicals, Inc. We study two popular one-dimensional chains of classical anharmonic oscillators: the rotor chain and a version of the discrete nonlinear Schrödinger chain. We assume that the interaction between neighboring oscillators, controlled by the parameter e{open}>0, is small. We rigorously establish that the thermal conductivity of the chains has a nonperturbative origin with respect to the coupling constant e{open}, and we provide strong evidence that it decays faster than any power law in e{open} as e{open}→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. To our knowledge, it is the first time that a clear connection has been established between KAM-like phenomena and thermal conductivity.