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Mean field theory is applied to nonequilibrium thermal energy transport in amodel molecular junction. An approximation to the total time-dependent heatcurrent in the junction is constructed using an ensemble of Ehrenfesttrajectories, and the average heat current in the steady state is obtained. Theaccuracy of this treatment is verified through benchmark comparisons with exactquantum mechanical results, and various approximate quantum transport theories,for the nonequilibrium spin-boson model. The performance of themulti-trajectory Ehrenfest approach is found to be quite robust, displayinggood accuracy in intermediate cases that remain elusive to many perturbativeapproximations, and in the strong coupling limit where many methods break down.Thus, mean field theory and related trajectory-based approximate quantumdynamics methods emerge as a promising toolkit for the study of transportproperties in nanoscale systems.

Mean Field Theory of Thermal Energy Transport in Molecular Junctions