Perturbative treatment of inter-site couplings in the local description of open quantum networks

Abstract: The problem of construction of a quantum master equation for a system of sites weakly coupled to each other and to one or more reservoirs (open quantum network) is considered. Microscopic derivation of a quantum master equation requires a diagonalization of the Hamiltonian of the network, which can be a difficult task. When the inter-site couplings are weak, the local approach, which neglects the influence of the inter-site couplings on the system-reservoir couplings, is often used. Recently, some doubts were cast to the consistency of the local approach. We develop a systematic perturbation expansion to derive corrections to the local approach and establish its range of validity. Using this extension of the local approach, we derive an expression for the heat flux for a particular model and show that it does not violate the second law of thermodynamics.