GQ corrections in the circuit theory of quantum transport

We develop a finite-element technique that allows one to evaluate correction of the order of GQ to various transport characteristics of arbitrary nanostructures. Common examples of such corrections are the weak-localization effect on conductance and universal conductance fluctuations. Our approach, however, is not restricted to conductance only. It allows one in the same manner to evaluate corrections to the noise characteristics, superconducting properties, strongly nonequilibrium transport, and transmission distribution. To enable such functionality, we consider Green’s functions of arbitrary matrix structure. We derive a finite-element technique from Cooperon and diffuson ladders for these Green’s functions. The derivation is supplemented with application examples. Those include transitions between ensembles and the Aharonov-Bohm effect.