Keldysh-Green function formalism for current profiles in mesoscopic systems

We provide a general procedure for the description and evaluation of the current distribution in mesoscopic quantum wires. Our approach is based on the Keldysh-Green function formalism of nonequilibrium quantum statistical mechanics and exploits the real-space renormalization method within the tight-binding framework. We obtain a detailed spatial description of the microscopic currents between any couple of sites of the system, both in the presence and in the absence of time-reversal symmetry. As an application we present current profiles for a disordered quantum wire in the regime of universal conductance fluctuations, and we illustrate the random path of the current flow also in the presence of a magnetic field.