Coupled harmonic systems as quantum buses in thermal environments

In this work, we perform a careful study of a special arrangement of coupled systems that consists of two external harmonic oscillators weakly coupled to an arbitrary network (data bus) of strongly interacting oscillators. Our aim is to establish simple effective Hamiltonians and Liouvillians allowing an accurate description of the dynamics of the external oscillators regardless of the topology of the network. By simple, we mean an effective description using just a few degrees of freedom. With the methodology developed here, we are able to treat general topologies and, under certain structural conditions, to also include the interaction with external environments. In order to illustrate the predictability of the simplified dynamics, we present a comparative study with the predictions of the numerically obtained exact description in the context of propagation of energy through the network.