Coherent transport in multibranch quantum circuits

An open multibranch quantum circuit is considered from the viewpoint of coherent electron or wave transport, both with and without intrinsic disorder. Starting with the closed system, we give analytical conditions for the appearance of two isolated localized states out of the energy band. In the open system, using the method of the effective non-Hermitian Hamiltonian, we study signal transmission through such a circuit, with an important result of a long lifetime of localized states. When the average level width becomes comparable to the mean level spacing, the superradiant transition occurs. In the case of onsite disorder, we find an analytical estimate, confirmed by numerical data, for the robustness of the isolated states and their role in transport processes.