Geometry-based atypical local energy current in semiclassical and quantum thermal transport

We use the semiclassical quantum thermal bath approach to reconcile the classical and quantum realms for thermal transport. In this method, we use Langevin equations within the molecular dynamics approach but with the reservoirs being quantum mechanical with Bose-Einstein statistics to calculate the local steady state thermal currents. We show that an atypical, local steady-state thermal current from cold to hot emerges in a classical harmonic system of Hookean springs and masses driven by two colored noise Langevin reservoirs at different temperatures in both the classical and quantum regimes for the system. In addition, for a full quantum treatment, we carry out the third quantization study of an equivalent quantum system and corroborate our results.