Keldysh Nonequilibrium Green Function
Current and spectral flow through a quantum dot under bias voltage
The Keldysh formalism treats nonequilibrium quantum transport via a time contour with forward and backward branches. For a quantum dot coupled to leads L,R with hybridizations Γ_L, Γ_R, the retarded Green function G^R(ω) = 1/(ω−ε₀+iΓ/2) gives spectral function A(ω) = Γ/((ω−ε₀)²+(Γ/2)²). The lesser Green function G^<(ω) = iA(ω)[Γ_L f_L+Γ_R f_R]/Γ encodes the nonequilibrium occupation. Current I = (e/h)∫dω Γ_L Γ_R/Γ · A(ω)(f_L−f_R).