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