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Meir-Wingreen formula for heat transport in a spin-boson nanojunction model

An analog of the Meir-Wingreen formula for the steady-state heat current through a model molecular junction is derived. The expression relates the heat current to correlation functions that involve operators only acting on the degrees of freedom of the molecular junction. As a result, the macroscopic heat reservoirs are not treated explicitly. This allows one to exploit methods based on a reduced description of the dynamics of a relatively small part of the overall system to evaluate the heat current through a molecular junction. The derived expression is applied to calculate the steady-state heat current in a weak coupling limit, where Redfield theory is used to describe the reduced dynamics of the molecular junction. The results are compared with those from the previously developed approximate and numerically exact methods.