

MAIN ACHIEVEMENTS:
 Derivation of the Kinetic Equations for System in a Thermal Bath within the
Method of Nonequilibrium Statistical Operator of D.N.Zubarev (1970);
 Derivation of the Schrodingertype Equation for a Dynamical System interacting with a Thermal Bath within the
Method of Nonequilibrium Statistical Operator of D.N.Zubarev (1970);
 Development of the Equationof motion Methods for the Doubletime Thermodynamic
Green Functions for the Strongly Interacting ManyParticle Systems on a Lattice;
 Formulation of the Method of Irreducible Green Functions for Interacting Fermions on a Lattice (19731975) ;
 New Selfconsistent Solution of the Strongly Correlated Hubbard Model (1975).
Derivation of the Generalized Twopole
Solution of the Hubbard Model which contains the HUBBARD III and Roth Solutions as Particular Cases (19751978);
 Studies of the Microscopic Models of Magnetism. Comparison of Itinerant and Localized Models of Magnetism.
Formulation of a Criterion for the Applicability of the Microscopic Model to Particular Material. The statement is that the Studies
of the Highenergy Excitations (Stoner Excitations) Can be Useful Mark for Providing Such a Criterion (19761982).
 In addition, some physical implications involved in a new concept, termed the
"quantum protectorate", were developed in 19992002. This was
done by considering the idea of quantum protectorate in the
context of quantum theory of magnetism. It was suggested that the
difficulties in the formulation of quantum theory of magnetism
at the microscopic level, that are related to the choice of
relevant models, can be understood better in the light of the "quantum protectorate"
concept . It was argued that the difficulties in the formulation of
adequate microscopic models of electron and magnetic properties of
materials are intimately related to dual, itinerant and localized
behaviour of electrons. A criterion of what basic
picture describes best this dual behaviour was formulated. The main suggestion
is that quasiparticle excitation spectra might provide
distinctive signatures and good criteria for the appropriate
choice of the relevant model.
 Formulation of the Selfconsistent Theory of the ElectronPhonon Interaction in Transition Metals, their Compounds
and Disordered Alloys within the Modified TightBinding Approximation(19791982);
 Derivation of the Strongcoupled Equations of Superconductivity for Transition Metals, their Compounds
and Disordered Alloys in the Wannier Representation(19801983);
 Formulation of the Consistent Theory of the
Transport Coefficients in Solids within the Nonequilibrium Statistical Operator Method. Investigation of the
resistivity of a model of transition metal with nonspherical Fermi surface. Clarification of the Role of
the ElectronPhonon Interaction for the Electroconductivity of Disordered Alloys (19791983);
 Theory of Quasiparticle Excitations in
Magnetic and Diluted Magnetic Semiconductors and Perovskite Manganites;
Selfconsistent Theory of the ElectronMagnon Interaction. Theory of Magnetic Polaron (19842005);
 Investigations of the Quasiparticle ManyBody Dynamics of the Basic Models
of Solid State Theory (19732005):
 Heisenberg Model, Heisenberg TwoSublattice Antiferromagnet,
 Hubbard Model,
 Anderson Model,
 s(d)f model and Kondo Lattice Model,
 Two and ManyImpurity Anderson Model;
 Interplay and Competition of Itinerant and Localized Magnetoactive Electrons in Solids (19982002);
 Theory of Layered HighTc Superconductors; Explanation of the Dependence of Transition Temperature on the Number of
Layers in the Mercurocuprates (19962003);
 Bound and Scattering States of Itinerant Charge Carriers in Complex Magnetic Materials (20042005);
 Generalized Kinetic and Evolution Equations in the Approach of the Nonequilibrium Statistical Operator (2005);
 Statistical Theory of Spin Relaxation and Diffusion in Solids (20052006);
 Transport Theory of Nonequilibrium Processes (2007);

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