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Feedback Network Models for Quantum Transport

Quantum feedback networks have been introduced in quantum optics as a set of rules for constructing arbitrary networks of quantum mechanical systems connected by uni-directional quantum optical fields, and has allowed for a system theoretic approach to open quantum optics systems. Our aim here is to establish a network theory for quantum transport systems where typically the mediating fields between systems are bi-directional. Mathematically this leads us to study quantum feedback networks where fields arrive at ports in input-output pairs, which is then just a specially case of the uni-directional theory. However, it is conceptually important to develop this theory in the context of quantum transport theory, and the resulting theory extends traditional approaches which tends to view the components in quantum transport as scatterers for the various fields, in the process allows us to consider emission and absorption of field quanta by these components. The quantum feedback network theory is applicable to both Bose and Fermi fields, moreover it applies to nonlinear dynamics for the component systems. In this first paper on the subject, we advance the general theory, but study the case of linear passive quantum components in some detail.