Aharonov-Bohm interferometry with quantum dots: scattering approach versus tunneling picture

We address the question of how to model electron transport through closed Aharonov-Bohm interferometers which contain quantum dots. By explicitly studying interferometers with one and two quantum dots, we establish the connection between a tunneling-Hamiltonian formulation on the one hand and a scattering-matrix approach on the other hand. We prove that, under certain circumstances, both approaches are equivalent, i.e., both types of models can describe the same experimental setups. Furthermore, we analyze how the interplay of the Aharonov-Bohm phase and the orbital phase associated with the lengths of the interferometers' arms affect transport properties.