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I am trying to calculate the conductivity in the linear response regime of a disordered electron gas. (or eventually of a mean field Heavy fermion system with known one particle green's functions).

I trying to use method in "Quantum field theory of non-equilibium states" by J.Rammer. Specifically I'm looking at section 6.2. Honestly, I don't understand very much of what he is doing. Have somebody done those calculations and could give guidelines on how to think and perhaps some more steps in the derivations?

My question in short would be: If I know the known free Green's functions, how do I calculate linear response when applying an electrical field?

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Rammer's book isn't quite what you need. In the linear response regime you relate the response to some applied field to equilibrium properties of the system absent the field. While the full theory of the non-equilibrium Green's functions will also let you calculate what you need, what you ought to be looking for is something called the "Kubo formula". – wsc Aug 2 '12 at 4:25
I have seen the Kubo formula. But it would be nice if one could derive the Kubo formula from the linear regime of the Dyson equations. The current can, as far as i know, be expressed in terms of the kinetic (Keldysh) Green's function. I don't understand how though. – Garvan Aug 2 '12 at 8:24

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