Heat Conduction in a Two-Dimensional Harmonic Crystal with Disorder

We study the problem of heat conduction in a mass-disordered two-dimensional harmonic crystal. Using two different stochastic heat baths, we perform simulations to determine the system size (L) dependence of the heat current (J). For white noise heat baths we find that J approximately 1/L(alpha) with alpha approximately equal to 0.59, while correlated noise heat baths give alpha approximately equal to 0.51. A special case with correlated disorder is studied analytically and gives alpha=3/2, which agrees also with results from exact numerics.