Quantum network approach to spin interferometry driven by Abelian and non-Abelian fields

We present a theory of conducting quantum networks that accounts for Abelian and non-Abelian fields acting on spin carriers. We apply this approach to model the conductance of mesoscopic spin interferometers of different geometry (such as squares and rings), reproducing recent experimental findings in pattered InAsGa quantum wells subject to Rashba spin-orbit and Zeeman fields. Moreover, by introducing some additional field-texture engineering, we manage to single out a previously unnoticed spin-phase suppression mechanisms. We observe that our approach also applies to the study of complex networks and the spectral properties of closed systems.