Nonequilibrium Green's function method for phonon-phonon interaction and   ballistic-diffusive thermal transport
  Phonon-phonon interaction is systematically studied by nonequilibrium Green's function (NEGF) formulism in momentum space at finite temperatures. Within the quasi-particle approximation, phonon frequency shift and lifetime are obtained from the retarded self-energy. The lowest order NEGF provides the same phonon lifetime as Fermi's golden rule. Thermal conductance is predicted by the Landauer formula with a phenomenological transmission function. The main advantage of our method is that it covers both ballistic and diffusive limits and thermal conductance of different system sizes can be easily obtained once the mode-dependent phonon mean free path is calculated by NEGF. As an illustration, the method is applied to two one-dimensional atom chain models (the FPU-\beta model and the \phi^4 model) with an additional harmonic on-site potential. The obtained thermal conductance is compared with that from a quasi-classical molecular dynamics method. The harmonic on-site potential is shown to remove the divergence of thermal conductivity in the FPU-\beta model. 
Yong Xu, Jian-Sheng Wang, Wenhui Duan, Bing-Lin Gu, and Baowen Li