Heat conduction in disordered harmonic lattices with energy conserving noise

We study heat conduction in a harmonic crystal whose bulk dynamics is supplemented by random reversals (flips) of the velocity of each particle at a rate $\lambda$. The system is maintained in a nonequilibrium stationary state(NESS) by contacts with Langevin reservoirs at different temperatures. We show that the one-body and pair correlations in this system are the same (after an appropriate mapping of parameters) as those obtained for a model with self-consistent reservoirs. This is true both for the case of equal and random(quenched) masses. While the heat conductivity in the NESS of the ordered system is known explicitly, much less is known about the random mass case. Here we investigate the random system, with velocity flips. We improve the bounds on the Green-Kubo conductivity obtained by C.Bernardin. The conductivity of the 1D system is then studied both numerically and analytically. This sheds some light on the effect of noise on the transport properties of systems with localized states caused by quenched disorder.