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 Ham
iltonian 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.
The state of art in the theoretical and experimental studies of transition metal doped oxides (dilute magnetic dielectrics) is reviewed. The available data show that the generic non-equilibrium state of oxide films doped with magnetic impurities may
either favor ferromagnetism with high Curie temperature or result in highly inhomogeneous state without long-range magnetic order. In both case concomitant defects (vacancies, interstitial ions play crucial part.
We consider the Kondo tunneling induced by multiphonon emission/absorption processes in magnetic molecular complexes with low-energy singlet-triplet spin gap and show that the number of assisting phonons may be changed by varying the Zeeman splitting
of excited triplet state. As a result, the structure of multiphonon Kondo resonances may be scanned by means of magnetic field tuning.
