$G_Q$-corrections in Circuit Theory of Quantum Transport
  We develop a finite-element technique that allows one to evaluate correction of the order of $G_Q$ to various transport characteristics of arbitrary nanostructures. Common examples of such corrections are weak localization effect on conductance and universal conductance fluctuations. Our approach, however, is not restricted to conductance only. It allows in the same manner to evaluate corrections to noise characteristics, superconducting properties, strongly non-equilibrium transport and transmission distribution. To enable such functionality, we consider Green 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 Aharonov-Bohm effect. 
G. Campagnano and Yu.V. Nazarov