In this paper we investigate the Anderson model applied to a quantum dot (QD) system in the Coulomb blockade regime. It is well known that such a system exhibits Kondo resonances for certain choices of parameters. Former studies heavily exploited large degeneracy of the f-levels [1, 2, 3] and spin dependence of the resonance has not been investigated [3]. We have used a different approach to the problem in which we describe the localized levels inside the QD in terms of Hubbard operators. By a diagrammatic scheme for Hubbard operators, similar to the iterative procedure by Kadanoff and Baym, we derive solutions of the model to the first order in transparency of the tunneling barriers. Already at this step we find that the poles of the QD Green function (GF) are given by an equation strikingly similar to the equation found by Lacroix [2] and Gunnarsson and Schoenhammar. However, the peculiarity found consists of the fact that a logarithmic renormalization of the QD level (and the corresponding density of state (DOS)), say with spin up, arises due to kinematic interactions with spin down electrons only. The logarithmic renormalization does not stem from the scattering on the Bose-like spin flip excitations in the standard Kondo effect. Instead, it is caused by fermion-fermion scattering. Besides, there is no requirement for the existence of a non-zero spin in the ground state of the QD. which leads to the conclusion that the observed resonance is not Kondo effect as it was suggested by [7].
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