Causal Green’s function for simulating phonon transport in 2-D solids: Application to graphene

A causal Green’s function method is described for simulating phonons and phonon transport in nanomaterials. In this method of modeling, the phonon term in the expansion of energy in atomic displacements is included exactly without any need for iterations. The phonons are simulated in terms of velocity autocorrelation functions, which represent collective modes of the crystal and not just single particle oscillations. For the purpose of demonstration, numerical results are presented for different cluster sizes and times ranging from femtoseconds to picoseconds. This range can be easily extended, if needed.