Heat Conduction in 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 ~ 1/L^a with $a \approx 0.59$ while correlated noise heat baths gives $a \approx 0.51$. A special case with correlated disorder is studied analytically and gives a=3/2 which agrees also with results from exact numerics.