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In the quantum transport, specially in calculating nano transistors' characteristics, we use a set of equations to find electron's density and specteral function. I want to know where they came from. The equations are :

[G]: Green's function matrix

[A(E)]: Spectral function

f1: fermi function in source

f2: fermi function in drain

H: Hamiltonian

[itex] [G] = [EI - H - \Sigma_{1} - \Sigma_{2} ]^{-1} [/itex]

Equ1: [itex] [A(E)] = i [G - G\dagger] [/itex]

Equ2: [itex] [G^{n}(E)] = [G \Gamma_{1} G \dagger] f1 + [G \Gamma_{2} G\dagger] f2 [/itex]

Could anyone say how I can prove these equations from Green's function definition?

Thanks

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# Quantum Transport Equations in Nanoelectronics

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