Microscopic model of a phononic refrigerator

We analyze a simple microscopic model to pump heat from a cold to a hot reservoir in a nanomechanical system. The model consists of a one-dimensional chain of masses and springs coupled to a back gate through which a time-dependent perturbation is applied. The action of the gate creates a moving phononic barrier by locally pinning a mass. We solve the problem numerically using a nonequilibrium Green's function technique. For low driving frequencies and for sharp traveling barriers, we show that this microscopic model realizes a phonon refrigerator.