Quantum non-locality in systems with open boundaries: From the Wigner-function formalism to non-homogeneous Markovian master equations

We shall discuss the role of electrical contacts within the conventional treatment of quantum devices based on the Wigner-Function formalism. Our analysis will show that the artificial spatial separation between device active region and external reservoirs, being intrinsically incompatible with the non-local character of quantum mechanics, may produce highly non-physical results like boundary-driven negative probability distributions. To overcome this serious limitation, we shall propose a new strategy to properly separate device and reservoir degrees of freedom, based on the well known projection techniques used in the formal theory of open systems. Our main result is a non-Markovian master equation, where dissipation and dephasing phenomena are also induced by the presence of spatially external particle reservoirs.