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The concept of dynamical symmetries is used for formulation of the renormalization group approach to the Kondo effect in the Anderson model with repulsive and attractive interaction $U$. It is shown that the generic local symmetry of the Anderson Hamiltonian is determined by the SU(4) Lie group. The Anderson Hamiltonian is rewritten in terms of the Gell-Mann matrices of the 4-th rank, which form the set of group generators and the basis for construction of irreducible vector operators describing the excitation spectra in the charge and spin sectors. The multistage Kondo sceening is described in terms of the local SU(4) dynamical symmetry. It is shown that the similarity between the conventional Kondo cotunneling effect for spin 1/2 in the positive $U$ model and the Kondo resonance for pair tunneling in the negative $U$ model is a direct manifestation of implicit SU(4) symmetry of the Anderson/Kondo model.
Usual paradigm in the theory of electron transport is related to the fact that the dielectric permittivity of the insulator is assumed to be constant, no time dispersion. We take into account the slow polarization dynamics of the dielectric layers in
Over-screened Kondo effect is feasible in carbon nanotube quantum dot junction hosting a spin $tfrac{1}{2}$ atom with single $s$-wave valence electron (e.g Au). The idea is to use the two valleys as two symmetry protected flavor quantum numbers $xi={
We study the possibility to observe the two channel Kondo physics in multiple quantum dot heterostructures in the presence of magnetic field. We show that a fine tuning of the coupling parameters of the system and an external magnetic field may stabi
The spatial length of the Kondo screening is still a controversial issue related to Kondo physics. While renormalization group and Bethe Anzats solutions have provided detailed information about the thermodynamics of magnetic impurities, they are ins
The tunneling conductance is calculated as a function of the gate voltage in wide temperature range for the single quantum dot systems with Coulomb interaction. We assume that two orbitals are active for the tunneling process. We show that the Kondo