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Phonon-phonon interaction is systematically studied by nonequilibrium Green'sfunction (NEGF) formulism in momentum space at finite temperatures. Within thequasi-particle approximation, phonon frequency shift and lifetime are obtainedfrom the retarded self-energy. The lowest order NEGF provides the same phononlifetime as Fermi's golden rule. Thermal conductance is predicted by theLandauer formula with a phenomenological transmission function. The mainadvantage of our method is that it covers both ballistic and diffusive limitsand thermal conductance of different system sizes can be easily obtained oncethe mode-dependent phonon mean free path is calculated by NEGF. As anillustration, 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-sitepotential. The obtained thermal conductance is compared with that from aquasi-classical molecular dynamics method. The harmonic on-site potential isshown to remove the divergence of thermal conductivity in the FPU-\beta model.

Nonequilibrium Green's function method for phonon-phonon interaction and ballistic-diffusive thermal transport