Thermal Conductivity for a Noisy Disordered Harmonic Chain

Abstract

We consider a $d$-dimensional disordered harmonic chain (DHC) perturbed by an energy conservative noise. We obtain uniform in the volume upper and lower bounds for the thermal conductivity defined through the Green-Kubo formula. These bounds indicate a positive finite conductivity. We prove also that the infinite volume homogenized Green-Kubo formula converges.

References in corpus (8)

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• Heat conduction in the disordered harmonic chain revisited
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Cited by in corpus (10)

• Non-equilibrium stationary state of a harmonic crystal with alternating masses
• Heat conduction in disordered harmonic lattices with energy conserving noise
• Energy transfer in a fast-slow Hamiltonian system
• Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions
• Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions
• Localization effects due to a random magnetic field on heat transport in a harmonic chain
• Thermalization of isolated harmonic networks under conservative noise
• Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise
• Homogenization results for a linear dynamics in random Glauber type environment
• Large-deviations approach to thermalization: the case of harmonic chains with conservative noise