The Kondo and the Fano resonances in the two-point Green's function of the single-level quantum dot were found and investigated in many previous works by means of different numerical calculation methods. In this report, we present a derivation of the analytical forms of the resonance terms in the expression of the two-point Green's function. For that purpose, the system of Dyson equations for the two-point nonequilibrium Green's functions in the complex-time Keldysh formalism was established to the second order in the tunneling coupling constants with the mean field approximation for the statistical averages of the products of four electron creation and destruction operators. This system of Dyson equations was solved exactly by means of the computer algebra and the analytical expressions for the resonance terms are derived. The conditions for the existence of the Kondo or the Fano resonances were found.

Van Hieu N., Ha N.B., Gerdt V.P., Chuluunbaatar O., Gusev A.A., Palii Yu.G., Van Hop N.

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