Thermal conductance for one dimensional disordered harmonic chains.*

We study heat conduction in one dimensional disordered harmonic chain of particles with longitudinal motion. We observe intriguing scaling behavior for the thermal conductance depending on the nature of the disorder and the coupling of the system with the heat bath. We show that the heat transport is 'anomalous' for an uniformly disordered chain, irrespective of the strength of the disorder and the coupling to the heat bath. Using a simple scaling relation, we show that thermal conductance scales with the system size (L) as L^{0.5} in this system. We further demonstrate that the scaling behavior for thermal conductance gets altered dramatically as we change the nature of the disorder. Particularly, we show that for disorder characterized by a 'heavy-tailed' probability distribution, the heat transport follows Fourier’s law when the coupling of the system with the thermal reservoir is weak. The different scaling behavior observed in the different models are shown to be intimately connected with the scaling properties of density of states and localization length of the phonons in the disordered systems.