# Mean Field Theory of Thermal Energy Transport in Molecular Junctions

## TL;DR

This paper applies mean field theory and Ehrenfest trajectories to model thermal energy transport in molecular junctions, demonstrating robustness and accuracy in regimes challenging for other methods.

## Contribution

It introduces a trajectory-based mean field approach for nonequilibrium thermal transport, validated against quantum benchmarks and applicable to complex regimes.

## Key findings

- Ehrenfest approach yields accurate steady-state heat currents.
- Method performs well in intermediate and strong coupling regimes.
- Robustness surpasses many perturbative quantum transport methods.

## Abstract

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.