Feedback network models for quantum transport

Quantum feedback networks have been introduced in quantum optics as a framework for constructing arbitrary networks of quantum mechanical systems connected by unidirectional 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 bidirectional. Mathematically, this leads us to study quantum feedback networks where fields arrive at ports in input-output pairs, making it a special case of the unidirectional theory where inputs and outputs are paired. However, it is conceptually important to develop this theory in the context of quantum transport theory-the resulting theory extends traditional approaches which tend to view the components in quantum transport as scatterers for the various fields, in the process allowing 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. We advance the general theory, but study the case of linear passive quantum components in some detail.