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Quantum Transport Equations in Nanoelectronics

  1. Jul 16, 2011 #1
    Hi Folks,

    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
     
    Last edited: Jul 16, 2011
  2. jcsd
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