Can Disorder Induce a Finite Thermal Conductivity in 1D Lattices?

We study heat conduction in one-dimensional mass-disordered harmonic and anharmonic lattices. It is found that the thermal conductivity kappa of the disordered anharmonic lattice is finite at low temperature, whereas it diverges as kappa approximately N0.43 at high temperature. Moreover, we demonstrate that a unique nonequilibrium stationary state in the disordered harmonic lattice does not exist at all.