Nonequilibrium functional bosonization of quantum wire networks

We develop a general approach to nonequilibrium nanostructures formed by one-dimensional channels coupled by tunnel junctions and/or by impurity scattering. The formalism is based on nonequilibrium version of functional bosonization. A central role in this approach is played by the Keldysh action that has a form reminiscent of the theory of full counting statistics. To proceed with evaluation of physical observables, we assume the weak-tunneling regime and develop a real-time instanton method. A detailed exposition of the formalism is supplemented by two important applications: (i) tunneling into a biased Luttinger liquid with an impurity, and (ii) quantum Hall Fabry–Pérot interferometry.

► A nonequilibrium functional bosonization framework for quantum wire networks is developed ► For the study of observables in the weak tunneling regime a real-time instanton method is elaborated. ► We consider tunneling into a biased Luttinger liquid with an impurity. ► We analyze electronic Fabry–Pérot interferometers in the integer quantum Hall regime.