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The review discusses the emergence of the spin-fermion model of cuprates and the formation of the spin-polaron concept of the electronic structure of hole-doped cuprate superconductors. This concept has allowed describing the properties of cuprates in the normal phase as well as the features of superconducting pairing in the unified approach. The derivation of the spin-fermion model from the Emery model in the regime of strong electronic correlations is described, demonstrating the appearance of strong coupling between the spins of copper ions and holes on oxygen ions. Such a strong interaction against the background of the singlet state of the spin subsystem of copper ions (quantum spin liquid) leads to the formation of special Fermi quasiparticles — nonlocal spin polarons. Under doping, the spin-polaron ensemble exhibits instability with respect to superconducting d-wave pairing, whereas superconducting s-wave pairing is not implemented. At the optimal doping, the transition to the superconducting phase occurs at temperatures corresponding to experimental data. It is shown that the superconducting d-wave pairing of spin-polaron quasiparticles is not suppressed by the Coulomb repulsion of holes located on neighboring oxygen ions. It is emphasized that, when the spec-tral characteristics of spin-polaron quasiparticles are taken into account, the calculated temperature and doping dependences of the London penetration depth are in good agreement with experimental data.

Taking into account the real crystalline structure of the $$\hbox {CuO}_2$$ plane within the spin-fermion model and using the diagram technique, the spin-polaron concept of the fermionic excitations in cuprate superconductors is implemented. It is shown that an account of the on-site scattering processes leads to considerable binding energy of the spin-polaron quasiparticles. An account of the two-site spin-fermion scattering processes results in the energy spectrum and spectral properties of the spin-polaron quasiparticles which agree well with experimental data on cuprate superconductors.

The Fermi excitation spectrum, the problem of Cooper instability, and the Londons magnetic field penetration depth in cuprate superconductors are considered using the unified conception based on accounting for the strong coupling between the spin of copper ions and holes at oxygen ions. This coupling leads to strong renormalization of the primary spectrum of oxygen holes with the formation of spin-polaron quasiparticles. Analysis of Cooper instability performed using the spin-polaron concept for different channels has shown that only the superconducting d-wave pairing occurs in the ensemble of spin-polaron quasiparticles, and there are no solutions corresponding to the s-wave pairing. It has been demonstrated that the superconducting d-wave pairing is not suppressed by the Coulomb repulsion of holes located at neighboring oxygen ions. This effect is due to peculiarities in the crystallographic structure of the CuO2 plane and the aforementioned strong spin–fermion coupling. As a result, such interaction of holes is omitted in the kernel of the integral equation for the superconducting order parameter with the d-wave symmetry. It has been shown the Hubbard repulsion of holes and their interaction for the second coordination sphere of the oxygen sublattice for actual intensities of the interaction do not suppress the d-wave type of superconductivity. For the spin-polaron ensemble, we have analyzed the dependence of the Londons magnetic field penetration depth on the temperature and hole concentration. It has been established that the peculiarities of this dependence are closely related to specific features of the spin-polaron spectrum.

The specific heat and susceptibilities for the two- and one-dimensional spin--orbital models are calculated in the framework of a spherically symmetric self-consistent approach at different temperatures and relations between the parameters of the system. It is shown that even in the absence of the long-range spin and orbital order, the system exhibits the features in the behavior of thermodynamic characteristics, which are typical of those manifesting themselves at phase transitions. Such features are attributed to the quantum entanglement of the coupled spin and orbital degrees of freedom., Comment: 7 pages, 9 figures, submitted to JETP Letters

Thermodynamic properties of the J1–J2–J3 quantum Heisenberg model are investigated on a square lattice with spin S = 1/2. The calculation of spin–spin correlators, spin excitation spectra, susceptibility, and heat capacity within a spherically symmetric approach shows that the third exchange J3 may qualitatively change the properties of the system. Along with standard short-range order (antiferromagnetic, ferromagnetic, and stripe) structures, various quantum helices arise. In particular, these structures may be isotropic with a local minimum of the spectrum along a circle in the Brillouin zone. The character of these states represents both ferromagnetic and antiferromagnetic “twisted” quantum spin ordering. Moreover, a range of parameters is determined in which heat capacity exhibits two-peak temperature behavior.

Taking into account the real crystalline structure of the $$\hbox {CuO}_2$$ plane and the strong spin-fermion coupling, we study the influence of the intersite Coulomb repulsion between holes on the Cooper instability of the spin-polaron quasiparticles in cuprate superconductors. The analysis shows that only the superconducting d-wave pairing is implemented in the whole region of doping, whereas the solutions of the self-consistent equations for the s-wave pairing are absent. It is shown that intersite Coulomb interaction $$V_1$$ between the holes located at the nearest oxygen ions does not affect the d-wave pairing, because its Fourier transform $$V_q$$ vanishes in the kernel of the corresponding integral equation. The intersite Coulomb interaction $$V_2$$ of quasiparticles located at the next-nearest oxygen ions does not vanish in the integral equations, however, but it is also shown that the d-wave pairing is robust toward this interaction for physically reasonable values of $$V_2$$ .

It is shown that for the three-band Emery p–d-model that reflects the real structure of the CuO2-plane of high-temperature superconductors in the regime of strong electron correlations, it is possible to carry out a sequence of reductions to the effective models reproducing low-energy features of elementary excitation spectrum and revealing the spin-polaron nature of the Fermi quasiparticles. The first reduction leads to the spin-fermion model in which the subsystem of spin moments, coupled by the exchange interaction and localized on copper ions, strongly interacts with oxygen holes. The second reduction deals with the transformation from the spin-fermion model to the φ–d-exchange model. An important feature of this transformation is the large energy of the φ–d-exchange coupling, which leads to the formation of spin polarons. The use of this fact allows us to carry out the third reduction, resulting in the t−J*−I-model. Its distinctive feature is the importance of spin-correlated hops as compared to th...

Mathematical models relating ultrasonically measured velocities and attenuation coefficients of sound to the basic physical and mechanical properties of rubbers were considered. The models were used for the development of methods for express quality assessment of rubber wastes. A compact universal minilaboratory for express analysis of rubber properties based on ultrasonic non-destructive control methods was offered.

The effect of the Coulomb repulsion of holes on the Cooper instability in an ensemble of spin–polaron quasiparticles has been analyzed, taking into account the peculiarities of the crystallographic structure of the CuO2 plane, which are associated with the presence of two oxygen ions and one copper ion in the unit cell, as well as the strong spin–fermion coupling. The investigation of the possibility of implementation of superconducting phases with d-wave and s-wave of the order parameter symmetry has shown that in the entire doping region only the d-wave pairing satisfies the self-consistency equations, while there is no solution for the s-wave pairing. This result completely corresponds to the experimental data on cuprate HTSC. It has been demonstrated analytically that the intersite Coulomb interaction does not affect the superconducting d-wave pairing, because its Fourier transform V q does not appear in the kernel of the corresponding integral equation.

Within the spin-fermion model for cuprate superconductors, the influence of the intersite Coulomb interactions $V_2$ and $V_2'$ between holes located at the next-nearest-neighbor oxygen ions of CuO$_2$ plane on the implementation of the d_{x^2-y^2}-wave pairing is studied. It is shown that d-wave pairing can be suppressed only for unphysically large values of $V_2$ and $V_2'$., 5 pages, 2 figures

The spin–fermion model, which is an effective low-energy realization of the three-band Emery model after passing to the Wannier representation for the px and py orbitals of the subsystem of oxygen ions, reduces to the generalized Kondo lattice model. A specific feature of this model is the existence of spin-correlated hoppings of the current carriers between distant cells. Numerical calculations of the spectrum of spin-electron excitations highlight the important role of the long-range spin-correlated hoppings.

Frustrated magnetic compounds, in particular low-dimensional, are topical research due to the persistent uncovering of novel nontrivial quantum states and potential applications. The problem of this field is that many important results are scattered over the localized parameter ranges, while areas in between still contain hidden interesting effects. We consider the [Formula: see text] Heisenberg model on the square lattice and use the spherically symmetric self-consistent approach for spin-spin Green's functions in 'quasielastic' approximation. We have found a new local order in spin liquids: antiferromagnetic isotropical helices. On the structure factor we see circular concentric dispersionless structures, while on any radial direction the excitation spectrum has 'roton' minima. That implies nontrivial magnetic excitations and consequences in magnetic susceptibility and thermodynamics. On the [Formula: see text] exchange parameters globe we discover a crossover between antiferromagnetic-like local order and ferromagnetic-like; we find stripe-like order in the middle. In fact, our 'quasielastic' approach allows investigation of the whole [Formula: see text] globe.

We address quantum spin helical states in the strongly frustrated Heisenberg model. Contrary to conventional Dzyaloshinskii–Moriya approach we show that such states appear without central symmetry breaking. As an example, we demonstrate that the magnetic and thermodynamic properties of the quasi-two-dimensional square-lattice compound (CuBr)Sr2Nb3O10 can be interpreted within 2D S = 1 ∕ 2 J 1 − J 2 − J 3 Heisenberg model. In this compound neutron experiment indicates helical spin order while central symmetry does hold.

Taking into account the concept of seamless integration, this paper presents the structural and functional scheme of information systems’ integration. The proposed scheme is specified for typical life cycle control systems of networks and electrical network equipment in information systems, with the dominant use of domestic software products. In the proposed scheme, the functional features and limitations of the module for controlling and correcting drawings, as well as the module for digitizing archive documentation, are clarified to form a unified system for digital prototyping of products in the context of a continuous lifecycle. We present the developed structure of the integrated information system for lifecycle support of networks and electrical network equipment. An integrated information system for lifecycle support implies the implementation of software in the form of a series of specialized platform-independent software intermodular interfaces, which allows for quick configuration of the system for the existing industry and enterprise specifics.

In the framework of the spin-fermion model, to which the Emery model is reduced in the limit of strong electron correlations, it is shown that the fermion quasiparticles in cuprate high-Tc superconductors (HTSCs) arise under a strong effect of exchange coupling between oxygen holes and spins of copper ions. This underlies the spin-polaron nature of fermion quasiparticles in cuprate HTSCs. The Cooper instability with respect to the d-wave symmetry of the order parameter is revealed for an ensemble of such quasiparticles. For the normal phase, the spin-polaron concept allows us to reproduce the fine details in the evolution of the Fermi surface with the changes in the doping level x observed in experiment for La2-xSrxCuO4. The calculated T–x phase diagram correlates well with the available experimental data for cuprate HTSCs.

We consider the evolution of the spectral function of charge carriers for a 2D Kondo lattice depending on the parameters of the model. A self-consistent solution is obtained for the spectral function using the formalism of irreducible Green’s functions. In the low doping level regime, the behavior of the spectral function exhibits suppression of the spectral weight of carriers in the low-frequency range, which is typical of the pseudogap state.

It has been shown that, because of the two-orbital character of the subsystem of holes located at oxygen sites and the spatial separation of this subsystem from that of spins at copper ions, the superconducting phase in high-T c superconductors is stable with respect to the strong Coulomb repulsion of holes located at nearestneighbor oxygen sites if the order parameter has the $${d_{{x^2} - {y^2}}}$$ symmetry. This effect is due to the symmetry characteristics of the Coulomb potential, owing to which the equation determining the Cooper pairing in the $${d_{{x^2} - {y^2}}}$$ channel does not include this potential.

In the framework of the spin-fermion model, it is shown that accounting for the strong spin-charge fluctuations between holes of copper and oxygen ions in cuprate High-T c superconductors leads to the formation of the Fermi spin-polaron quasiparticles. It is demonstrated that the large value of the binding energy of such quasiparticle is determined by the processes in which hopping intensity of the oxygen holes depends significantly on the spin configuration of holes on the copper and oxygen ions. It was found that the ensemble of such quasiparticles manifests Cooper instability and the concentration dependence of the critical temperature is in good agreement with the experimental data.

A matrix projection formalism is developed for the description of a frustrated two-dimensional antiferromagnet. This approach keeps safe all the advantages of the spherically symmetric self-consistent treatment (it strictly meets the spin constraint and the Mermin—Wagner theorem) but does not have its disadvantages. In particular, even in its simplest implementation, this approach provides a good agreement with the numerical simulations for two best-studied reference points: the zero frustration point and the point of a transition from the antiferromagnetic ordered phase to the disordered phase.

In a spherically symmetric self-consistent approach (SSSA), the spin-1/2 J 1–J 2 Heisenberg model on a two-dimensional square lattice is considered for two-time retarded spin–spin Green’s functions. The spin excitation spectrum, ω(q), and spin gaps at symmetric points are obtained for the entire J 1–J 2 diagram, i.e., for any ϕ, J 1 = cosϕ, and J 2 = sinϕ. The structure factor c q and the correlation length ξ at finite temperature are calculated in the entire range of parameters. A radical difference in the behavior of the system in the upper, frustrated (0 ⩽ ϕ ⩽ π), and the lower, nonfrustrated (π ⩽ ϕ ⩽ 2π), regions of the diagram is demonstrated. In the latter region, there is a first-order phase transition that is unique on the phase diagram. For a weakly frustrated antiferromagnet (J 1 > J 2 > 0), the results obtained are compared with the experimental dependence of ξ on temperature and doping level. A correspondence rule is proposed between frustration in a spin model and the doping of an antiferromagnet with holes.

It is shown that the exchange interaction in the subsystem of localized moments of copper ions can trigger a Cooper instability in the ensemble of spin-polaron quasiparticles in cuprate high-temperature superconductors. It is important that, inherent to cuprates, strong coupling between Fermi and spin degrees of freedom leads on the one hand to formation of spin-polaron quasiparticles and, on the other hand, allows to transfer the interaction between Bose degrees of freedom onto the interaction between Fermi quasiparticles. The solution of the integral equation for the d-wave superconducting order parameter is well consistent with the available experimental data.

The paper describes the conditional management technology for the coordinated interaction of software agents in the integrated information space of an enterprise.

We draw attention to a similarity between mutually related kinetic material phenomena that are odd in the magnetic field and produce an electric current or heat flow perpendicular (1) to the magnetic field, (2) to the electric field strength or to the temperature gradient. These phenomena include the Hall effect, the Righi–Leduc effect in nonmagnetic metals, the anomalous Hall effect in magnets, the odd Senftleben–Beenakker effect in molecular gases, and the phonon Hall effect in dielectrics. While these phenomena have much in common in terms of geometry, their formation mechanisms — dynamic and dissipative — are different. However, in all cases, the flow perpendicular to the magnetic field arises from the spin-orbit interaction of carriers with magnetic moments.

It is demonstrated for the first time that the strong coupling between spin moments of copper ions and oxygen holes, which arises upon hybridization mixing of two hole subsystems in the Emery model, not only affects the formation of spin polaron quasiparticles but also ensures effective attraction between them via the exchange interaction. This results in the Cooper instability with d-wave pairing in a 2D ensemble of spin polaron quasiparticles. The T – x phase diagram obtained using this approach agrees well with the available experimental data.

For a two-dimensional optimally doped antiferromagnet with spin S =1/2, we study the temperature dependence of the electrical resistivity ρ(T), Hall coefficient RH(T), and thermopower Q(T). The temperature dependence corresponding to optimally doped layered high-Tc superconducting cuprates has been obtained simultaneously for all three transport coefficients within the unified spin-polaron approach for the Kondo lattice. The key features of our study are the usage of the multimoment method for solving the kinetic equations (seven moments for the nonequilibrium distribution function ensure a good convergence) and the form of ac spin susceptibility χ(q, ω) for localized spins. For χ(q, ω), we choose a self-consistent expression which takes into account the “crossover” between the spin susceptibility determined by the self-consistent spherically symmetric Green’s function method and the semiphenomenological spin susceptibility corresponding to the critical decay of magnons.

This paper considers general gradient definition rules in modeling of control systems for complex objects in the case of accurate gradient estimation using adjoint systems.

This paper states the evolutionary approach to constructing models of control and decision-making. The approach is grounded on the most general principles of functioning in biological systems, namely, the principles of modularity, multilevel and multi-alternativeness. And finally, the authors consider some directions of implementing these principles in models of intelligent control systems using neural network technology.

It is shown using the 2D Emery model that the strong coupling between the spin subsystem of copper ions in the singlet state and the subsystem of oxygen holes considerably reduces the spectral intensity of the correlation function for holes on the Fermi contour. Spin-charge correlations are manifested in the existence of two channels. The first channel is due to the p-d exchange coupling of spins of the oxygen and copper holes. The second channel appears as a result of spin-correlated hoppings, when the motion of holes over oxygen ions is accompanied by spin-flip processes (i.e., simultaneous changes in the spin projections of an oxygen hole and a copper ion). It is established as a result of self-consistent calculations that the allowance for the concentration dependence of spin correlators and multicenter spin-charge correlators appearing in the dispersion equation ensures a decrease in the energy of the system and considerably affects the evolution of the Fermi surface under hole doping.

For the spin-fermion model, it has been shown that the concept of spin polarons makes it possible to reproduce fine details of the Fermi surface evolution in the nodal direction of La2 − xSrxCuO4 occurring with changes in the doping level x. The physics here is determined by the spin-correlated hopping of charge carriers and by the doping dependence of the inverse magnetic correlation length.

It is shown that the strong coupling between spin moments of copper ions and oxygen holes resulting from the hybridization processes in the Emery model determines the formation of spin-polaron quasiparticles and ensures their effective attraction. This induces Cooper instability with d-wave pairing of spinpolaron quasiparticles. The obtained phase diagram agrees with the available experimental data.

The ground state of the J 1-J 2 Heisenberg model with arbitrary signs of exchange is studied for spin S = 1/2 in the case of the two-dimensional (2D) square lattice. The states with different types of spin long-range order (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as the disordered spin liquid states are described in the framework of one analytical approach. In particular, it is shown that the phase transition between the ferromagnetic spin liquid and the ferromagnet with long-range order is of the second order. In the vicinity of such transition, we have found the ferromagnetic state with a rapidly varying condensate function.

In the spherically symmetric self-consistent approach to spin–spin Green’s functions, we consider a two-dimensional strongly frustrated J 1 − J 2 − J 3 quantum S = 1 / 2 antiferromagnet. In the classical limit S ≫ 1 , the phase diagram of the model demonstrates two triple points. We show that, in the quantum limit S = 1 / 2 for J 3 0 , a quadruple point of the quantum phase transition appears. At this point, the four coexisting phases are a disordered spin-liquid phase and three phases with different types of long-range order. Two of them are well-known “checkerboard” Neel order and stripe order; the last one corresponds to a non-trivial state with two coexisting mutually penetrating long-range orders.

An orthonormalized basis describing the single-hole states of the CuO2 plane has been constructed exactly taking into account the p-d exchange coupling between the spins of a hole and the two nearest copper ions. The introduced basis makes it possible to include the effects caused by the dependence of the Heisenberg interaction between the nearest copper ions on the occupation of the intermediate oxygen ion by the hole in the calculation of the spectrum of the collective excitations of nonlocal three-spin polarons. The inclusion of this correlation, as well as the nonlocality of the p-d exchange coupling, is the main difference of the developed approach to the description of the energy structure from the calculations with the use of the Zhang-Rice singlet.

The normal and superconducting phases of the ensemble of spin polarons in a two-dimensional Kondo lattice have been considered under the conditions when the hopping integral is comparable to the s-d exchange interaction energy. The polaron excitation spectrum and the superconducting transition temperature have been found taking into account upper triplet states. The change in the concentration dependence of the critical temperature of the transition to the superconducting phase with the relation between the hopping integral and the integral of the s-d exchange coupling has been analyzed.

In the framework of a spherically symmetric self-consistent approach to two-time retarded spin-spin Green’s functions, we develop the theory of a two-dimensional frustrated J1-J2-J3 quantum S=1/2 antiferromagnet. We show that taking the damping of spin fluctuations into account is decisive in forming both the spin-liquid state and the state with long-range order. In particular, the existence of damping allows explaining the scaling behavior of the susceptibility χ(q, ω) of the CuO2 cuprate plane, the behavior of the spin spectrum in the two-plane case, and the occurrence of an incommensurable χ(q, ω) peak. In the case of the complete J1-J2-J3 model, in a single analytic approach, we find continuous transitions between three phases with long-range order (“checkerboard,” stripe, and helical (q, q) phases) through the spin-liquid state. We obtain good agreement with cluster computations for the J1-J2-J3 model and agreement with the neutron scattering data for the J1-J2 model of cuprates.

The phase diagram of the frustrated J 1-J 2-J 3 S = 1/2 Heisenberg model on a square lattice is studied in the range of parameters corresponding to the spin-liquid state of the system. The study is performed using the self-consistent two-time retarded spin-spin Green’s functions, which do not break both translational and SU(2) symmetries. The inclusion of the damping of spin fluctuations allows us to obtain a good agreement with the cluster calculations. Using a consistent analytical approach, we have found continuous transitions via the spin-liquid state between the phases with three types of the long-range order: checkerboard, stripe, and (k, k) helical. In addition, there are indications confirming the existence of the (k, π) helical phase.

The pseudogap behavior of spectral function A(k, ω) of charge carriers is considered in the weak doping regime for a 2D Kondo lattice with a strong spin-hole antiferromagnetic interaction. The scattering of carriers is described in terms of a local polaron according to the irreducible Green functions. The behavior of the carrier spectrum in the nodal and antinodal domains is considered. The resultant value of the pseudogap is in conformity with experimental data on photoemission with angular resolution.

A cluster problem is analyzed as an example demonstrating that the observed three-mode behavior of spin-triplet excitations in YbB12 can be described by the asymmetric Anderson model with insulating singlet ground state. In the case of an infinite system, it is argued that the behavior of the f subsystem can be analyzed by using an effective Hamiltonian ĤJ with direct antiferromagnetic f-f exchange interaction. The spin excitation spectrum is shown to have a minimum at the antiferromagnetic vector, as observed experimentally. A distinctive feature of the analysis is the use of singlet and triplet basis operators.

Cluster based analysis show that the observable three-level YbB 12 spin excitations character can be reproduced in the framework of the asymmetric variant of periodic Anderson model with a singlet ground state and two electrons per site. For the macroscopic system the effective Hamiltonian with the direct f – f exchange is justified and the dynamic spin susceptibility of f -electrons is found. It is shown that the lowest spin excitation dispersion has minimum at the antiferromagnetic vector as observed in the experiment. The distinctive feature of analysis is the using of singlet and triplet basis operators.

The influence of damping on the phase diagram of two-dimensional S=1/2S=1/2 frustrated Heisenberg model is investigated. The damping is introduced semiphenomenologically in the frames of self-consistent spherically-symmetric approach for spin Green's functions. The comparison of the results with numerical calculations shows that the damping γ is significant (γ∼0.5γ∼0.5) at the point of checkerboard long-range loss (frustration parameter p≃0.275p≃0.275). The role of the vertex corrections is also investigated.

It has been shown that two-and three-center interactions arise in the strong-coupling regime for the 2D Kondo lattice; these interactions both induce and suppress the Cooper instability. It is important that, in contrast to the t-J* model, the three-center interactions promote the Cooper pairing and ensure the appearance of the superconducting phase with a high critical temperature Tc. The calculated concentration dependences of Tc agree well with the experimental data for the cuprate superconductors.

A scientific outreach session of the Physical Sciences Division of the Russian Academy of Sciences (RAS) was held on 23 April 2008 at the Institute for High Pressure Physics, RAS, Troitsk, Moscow region. The session was devoted to the 50th anniversary of the Institute. The following reports were presented: (1) Stishov S M (Institute for High Pressure Physics, RAS, Troitsk, Moscow region) "The Institute for High Pressure Physics is now 50 (opening address)"; (2) Khvostantsev L G and Slesarev V N (Institute for High Pressure Physics, RAS, Troitsk, Moscow region) "Large-volume high-pressure devices for physical investigations"; (3) Popova S V, Brazhkin V V and Dyuzheva T I (Institute for High Pressure Physics, RAS, Troitsk, Moscow region) "Structural phase transitions in highly compressed substances and the synthesis of high-pressure phases"; (4) Dzhavadov L N, Gromnitskaya E L, Stepanov G N and Timofeev Yu A (Institute for High Pressure Physics, RAS, Troitsk, Moscow region) "Studies of the thermodynamic, elastic, superconducting, and magnetic properties of substances at high pressures"; (5) Dizhur E M, Venttsel V A and Voronovskii A N (Institute for High Pressure Physics, RAS, Troitsk, Moscow region), "Quantum transport at high pressures"; (6) Ryzhov V N, Barabanov A F, Magnitskaya M V and Tareyeva E E (Institute for High Pressure Physics, RAS, Troitsk, Moscow region) "Theoretical studies of condensed matter"; (7) Bugakov V I, Antanovich A A, Konyaev Yu S and Slesarev V N (Institute for High Pressure Physics, RAS, Troitsk, Moscow region) "Designing new construction and superhard materials and related tools." An abridged version of reports 1 –6 is presented below. • The Institute for High Pressure Physics is now 50 (opening address), Stishov S M Physics-Uspekhi, 2008, Volume 51, Number 10, Pages 1055-1059 • Large-volume high-pressure devices for physical investigations, Khvostantsev L G and Slesarev V N Physics-Uspekhi, 2008, Volume 51, Number 10, Pages 1059-1063 • Structural phase transitions in highly compressed substances and the synthesis of high-pressure phases, Popova S V, Brazhkin V V and Dyuzheva T I Physics-Uspekhi, 2008, Volume 51, Number 10, Pages 1064-1066 • Studies of the thermodynamic, elastic, superconducting, and magnetic properties of substances at high pressures, Dzhavadov L N, Gromnitskaya E L, Stepanov G and Timofeev Yu A Physics-Uspekhi, 2008, Volume 51, Number 10, Pages 1066-1070 • Quantum transport at high pressures, Dizhur E M, Venttsel V A and Voronovskii A N Physics-Uspekhi, 2008, Volume 51, Number 10, Pages 1070-1077 • Theoretical studies of condensed matter, Ryzhov V N, Barabanov A F, Magnitskaya M V and Tareyeva E E Physics-Uspekhi, 2008, Volume 51, Number 10, Pages 1077-1083

In the Kondo model of the two-dimensional lattice with a strong spin-hole antiferromagnetic exchange, the pseudogap behavior of the carrier spectral function A(k, ω) is considered in the optimal and almost dielectric doping limits. A distinctive feature of the analysis is the introduction of the spin polaron even in the mean-field approximation that leads to the formation of two bands (the analogs of the upper and lower Hubbard bands) and makes it possible to immediately take into account the main rearrangement of A(k, ω). The inclusion of the scattering of the mean-field polaron (within the irreducible Green’s functions) describes the further rearrangement of A(k, ω), in particular, the unusual appearance of the pseudogap near the points N = (±π/2, ±π/2).

Experimental data on the non-spin-wave behavior of the cuprate magnetic susceptibility χ(q, ω) in the superconducting state are reconstructed on the basis of a spherically symmetric self-consistent approach within the framework of the frustrated Heisenberg model. For the Green’s function of the spin-wave excitations, a polarization operator resonant with the superconducting state is introduced phenomenologically. This gives rise to an additional (compared to the normal state) branch of the incommensurate peaks and to a pronounced non-spin-wave behavior of the susceptibility χ(q, ω) in the frequency range near 80 meV (the so-called “dark region”). The renormalization of the real part of the polarization operator plays a crucial role in the theory.