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This review deals with the nonequilibrium Green's function (NEGF) methodapplied to the problems of energy transport due to atomic vibrations (phonons),primarily for small junction systems. We present a pedagogical introduction tothe subject, deriving some of the well-known results such as the Laudauer-likeformula for heat current in ballistic systems. The main aim of the review is tobuild the machinery of the method so that it can be applied to othersituations, which are not directly treated here. In addition to the above, weconsider a number of applications of NEGF, not in routine model systemcalculations, but in a few new aspects showing the power and usefulness of theformalism. In particular, we discuss the problems of multiple leads, coupledleft-right-lead system, and system without a center. We also apply the methodto the problem of full counting statistics. In the case of nonlinear systems,we make general comments on the thermal expansion effect, phonon relaxationtime, and a certain class of mean-field approximations. Lastly, we examine therelationship between NEGF, reduced density matrix, and master equationapproaches to thermal transport.

Nonequilibrium Green's function method for quantum thermal transport