Disordered harmonic chain with self-consistent reservoirs

Abstract

Exact calculations of heat flows and thermal conductivities in disordered harmonic chains of up to 50 atoms have been made within the framework of the self-consistent reservoir model. Thermal conductivities, obeying Fourier's law, are given as functions of the coupling to the internal heat baths for both fixed-end and free-end boundary conditions. On the basis of these calculations, it is conjectured that an infinite disordered chain with only harmonic interactions may, indeed, retain a unique finite thermal conductivity in the limit that the internal reservoir coupling goes to zero.