The Quantum Theory of Conductivity of Spatially - Heterogeneous Systems
  The quantum theory of conductivity of semiconductor objects, to which the quantum wells, wires and dots concern, is constructed. Average values of current and charge densities, induced by a weak electromagnetic field, are calculated. It is shown, that in both cases average current and charge densities contain two contributions, first of which is expressed through electric field, and second - through a spatial derivative of electric field. Appropriate expressions for the conductivity tensor, dependent on coordinates and applicable to any spatially-heterogeneous systems, are deduced. The results may be used in the theory of secondary light radiation from low-dimensional objects in cases of monochromatic light and light pulses. 
I.G.Lang, L.I. Korovin, J.A.de la Cruz Alcaz and S.T.Pavlov