  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.
