Composite Non-equilibrium Environments

Abstract

This chapter discusses models that assume a stationary non-equilibrium steady state without any external interventions. Mostly, these may be implemented by electronic setups, e.g., with transport through quantum dots or molecules, but the general machinery is also applicable to quantum optical setups. We first investigate the single electron transistor (SET) and afterwards the double quantum dot (DQD) with a focus on the thermodynamic interpretation. To mimic the interaction of such systems with a charge detector, we afterwards consider interacting transport channels: two coupled SETs and an SET coupled to a low-transparency quantum point contact (QPC). We discuss the decoherence of a charge qubit induced by a QPC. As an example for a setup where the environment itself is in a non-equilibrium steady state that cannot be expressed as a simple tensor product of different equilibrium states, we discuss an SET (which is solved exactly) weakly coupled to a DQD. We conclude by discussing models involving bosons and fermions simultaneously: this includes a model where phonon-assisted tunneling may be exploited to implement a thermoelectric generator. Finally, we present a model where—despite the strong coupling between the electronic system and the bosonic reservoir—a description within a simple rate equation is still possible. Despite its low dimensionality, the model allows for a rich dynamics and inspiring thermodynamic interpretation.