A NON-PERTURBATIVE GREEN FUNCTION TECHNIQUE FOR CALCULATIONS OF NON-LINEAR TRANSPORT PROPERTIES

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Abstract
We have developed a Green function formalism to calculate transport properties in an arbitrarily strong static electric field. In the special case where an isolated resonant level is coupled to the conduction electrons our formalism has permitted an exact analytical evaluation of the single particle Green function. Our results can be characterized in terms of the T-matrix whose imaginary part (in zero electric field) gives the scattering rate. We find T(ε) = V02/[ε-E-iƉ], where E is the energy of the resonant level and F is the electric field. The width function Ɖ (ε, F) is a measure of the coupling of the conduction electrons to the resonant level. For a gaussian impurity potential we demonstrate analytically the transition from collision dominated to free particle behavior as the electric field is increased

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