In the magnetically diluted LaMn_xGa_1-xO₃ single crystals, the EPR spectra of the Mn ions (at 0.02 <=  x <= 1), as well as NMR and nuclear spin-lattice relaxation of ⁶⁹Ga and ⁷¹Ga nuclei have been investigated. The analysis of the EPR spectra enabled one to follow the exchange narrowing effect to the point of appearance of a single Lorentzian line at x  >=  0.2. The transition from the antiferromagnetic to ferromagnetic type of spin ordering is confirmed under condition of the diamagnetic dilution with Ga, starting from x  = 0.8. At x  = 0.1, unusual broadening and splitting of the EPR spectrum are found upon cooling; this can be assigned to the effect of thermally activated internal motion with characteristic energy E_a of about 50 meV. The study of nuclear spin-lattice relaxation was performed in the temperature range of 190-390 K. The obtained data support the existence of the internal motion with the same value of E_a . This motion can be attributed to thermally activated re-orientations of the e_g electron orbitals of the Mn³⁺ ions subjected to the Jahn-Teller effect.

The two-orbital Hubbard model is used to obtain formula for the fermion excitation spectrum in the energy bands hybridized by Anderson’s interaction. A transition to the Hubbard operators diagonalizes the one-site part of the Hamiltonian and allows us to use Green’s function technique to take into account the interstitial hopping term, while studying the superconducting properties of the model. By proposing the dependence of the matrix element responsible for hybridization of p- and d- electronic states on the ampltitude of local vibrations of ions, we determined a value of isotopic effect a = ( M / T_c ) ( dT_c / dM ) (M – mass of ions). The dependence of a upon carrier density and energy parameters determining the intra-atomic correlation is analyzed. It was concluded, that at some values of parameters the isotopic effect in T_c can be large enough and the model under consideration can be used for the description of the isotopic shift in T_c for a number of superconductors.

The inhomogeneous skyrmion states of two-dimensional classical ferromagnet were shown to be stable spin cofigurations. The energy spectrum of elementary excitations above the skyrmion background was obtained.

Starting from the three-band p-d Hubbard Hamiltonian we derive the effective t-J model Hamiltonian including electron-phonon interaction of quasiparticles with optical phonons and strong electron correlations. We consider two possible cases when the carriers move over the oxygen sites and also if the they move over the copper sublattice. Most importantly, we find that the phonon renormalization of t is quite different in both cases. Within an effective Hamiltonian we analyze the influence of phonons on the dynamical spin susceptibility in layered cuprates. For example, we find an isotope effect on resonance peak in the magnetic spin susceptibility, Im\chi(q,\omega), seen by inelastic neutron scattering. It experimental observation would be a strong argument in favor of polaronic character of the carrier motion in layered cuprates.

Mutual uncrossability of polymer chains and low compressibility of polymer melts give rise to dynamical correlations between polymer segments of different chains, separated by distances much larger than typical sizes of macromolecules. Due to this the terminal relaxation time  τ₁ ∝ N^13/4  and self-diffusion coefficient  D  ∝ N ^{- 9/4}  have the strong molecularmass dependencies. 

We use transformation properties of the irreducible representations of the symmetry group of the Hamiltonian and properties of a continuous path to define a "failure tree" procedure for finding eigenvalues of the Schrodinger equation using stochastic methods. The procedure is used to calculate energies of the lowest excited states of quantum systems possessing anti-symmetric nodal regions in configuration space with the Feynman-Kac path integral method. Within this method, the solution of the imaginary time Schrodinger equation is approximated by random walk simulations on a discrete grid constrained only by symmetry considerations of the Hamiltonian. The required symmetry constraints on random walk simulations are associated with a given irreducible representation of a subgroup of the symmetry group of the Hamiltonian and are found by identifying the eigenvalues for the irreducible representation corresponding to symmetric or antisymmetric eigenfunctions for each group operator. As a consequence, the sign problem for fermions is eliminated. The method provides exact eigenvalues of excited states in the limit of infinitesimal step size and infinite time. The numerical method is applied to compute the eigenvalues of the lowest excited states of the hydrogenic and helium atoms.

We have performed ferromagnetic resonance (FMR) studies of epitaxial V/Pd_1-xFe_x (001) bilayers with a V thickness of the order of 40 nm and with a Pd_1-xFe_x thickness in the range from 0.8 nm to 4.4 nm. For a bilayer with a Pd_1-xFe_x thickness of 1.2 nm and x = 0.03 the FMR measurements revealed a decrease of the effective magnetization 4$\pi M_eff$ of the ferromagnetic layer below the superconducting transition temperature of vanadium. As a possible explanation for this decrease we suggest a spatial modulation of the ferromagnetic order in the Pd_1-xFe_x layer due to modifications of the indirect exchange interaction of magnetic ions via conduction electrons in the superconducting state. A comparison with a recent theoretical investigation supports this possibility.

Method of generating functional is developed for the Hubbard model in the case of strong electron correlations. The method is a generalization of the Kadanoff-Baym approach, suggested earlier for conventional fermi-systems, to highly correlated systems. The method deals with equations for electron Green's functions in terms of variational derivatives with respect to fluctuating fields. In the exact equations a mean-field approximation is suggested with taking into account the static fluctuations of charge and spin. Interrelation between this method and the method of composite operators is established. It is shown that a two-poles approximation for the electronic Green's function describes essential features of quasiparticle spectrum and its evolution when changing electron concentration n and on-site Coulomb interaction U . At half-filling ( n  = 1) at U = U _c   ~  1.73 W ( W – width of the bare electron band) a phase transition metal-insulator occurs .

We present the analysis of the behavior of interacting fermions near the Stoner instability in a Fermi liquid. We show that the Landau damping of the spin susceptibility is a relevant perturbation near the quantum critical point, and it gives rise to the effective locality of the problem – fermionic self-energy near the transition strongly depends on frequency, but weakly depends on momentum. We discuss how Fermi liquid behavior gradually disappears near the transition in D  <= 3, and present the results for the fermionic self-energy at the critical point.

We study the effect of random porous matrices on the isotropic- nematic phase transition. Sufficiently close to the cleaning temperature, both random field and thermal fluctuations are important as disordering agents. A novel random field fixed point of renormalization group equation was found that controls the transition from isotropic to the replica symmetric phase. Explicit evaluation of the exponents in d  = 6 – ε dimensions yields to a dimensional reduction and three-exponent scaling.

For the layered ferromagnetic metal/superconductor (FM/S) structures new boundary-value problem, which takes into account a competition between the one-dimensional (1D) and three-dimensional (3D) realizations of the Larkin-Ovchinnikov-Fulde-Ferrell states, is derived. Superconductivity in the FM/S structures proves to be a superposition of the BCS pairing with zero total momentum in the S layers and the FFLO paring with nonzero pair momentum k in the FM layers. It is shown that processes of transition and mutual transformation of the BCS and FFLO pairs at the FM/S boundary occur as the Umklapp processes during which the coherent pair momentum k is conserved with exactness up to the reciprocal LOFF lattice vector G . These Umklapp processes can occur both in normal (1D states) and in the tangent (3D states) directions with respect to the FM/S interface. It is found that nonmonotonic behavior of the critical temperature T_c in the FM/S billayers is caused by the oscillations of the Cooper pairs flux through the S/FM boundary due to 3D-1D-3D phase transition cascade and switching between normal and tangent Umklapp processes. For the FM/S superlattices the existence of new π-magnetic 0π and ππ LOFF states, which at certain conditions can have a much higher T_c than earlier known 0-magnetic 00 and π0 LOFF states, is discovered. The T_c nonmonotony in the FM/S superlattices may be due to the 3D(0π)-1D(ππ)-3D(ππ) phase transitions cascade at small S interlayer thickness or due to another chain of the 3D(00)-1D(π0)-3D(π0) transitions at larger S interlayer thickness.

As an ensemble scheme of solid-state NMR quantum computers the scheme based on the array of ³¹P donor atoms which are spaced lengthwise of the strip gates is considered. The possible planar topology of such ensemble quantum computer is suggested. The estimation of the output NMR signal is performed and it is shown that for the number N >= 10⁵ of ensemble elements involving L ~10³ qubits each, the standard NMR methods are usable. As main mechanisms of decoherence for low temperature (< 0.1  K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin hyperfine interaction with electron magnetic moment of basic atom and dipole-dipole interaction with nuclear moments of neighboring impurity atoms was considered, Estimations of allowed concentrations of magnetic impurities and of spin temperature whereby the required decoherence suppression are obtained. Semiclassical decoherence model of two qubit entangled states is also presented.

The model of the normal flux core of the Abrikosov's vortex in a type II superconductor is used (κ >>1, k is the Ginzburg-Landau parameter). It is shown, that on the basis of the quantum-mechanical generalization of the London's equation for the superconducting current with the supposition of the normal flux core the equations for the magnetic field rearrange to the form of generalized London's equation (with an accuracy 1/κ). Solutions of generalized London 's equation are obtained for a single vortex in infinite superconductor and for the vortex lattice in a semi-infinite superconductor. It is shown, that these solutions are finite in any point of the space and that the removal of divergences is getting automatically. The normal flux core model offers an advantage over the Clem's model, so that it allows to solve the boundary-value problem more successfully for the vortex lattice of the superconducting semispace.

We investigate the B-U-V Hubbard model in the Static-Fluctuation Approximation. The first part of the article is devoted to the exact solution of the Hubbard model in the case of two sites of the crystal lattice. We got and solved system of 24 differential equations for the 24 Fermi operators. The anticommutator Green's function for dimer was derived. In the second part we calculate the anticommutator Green's function for dimer in the Static-Fluctuation Approximation. Comparison of the exact and approximate solutions shows that the Static-Fluctuation Approximation adequately describes the Hubbard model for case of two sites of the crystal lattice. The third part is concerned with the solution in the Static-Fluctuation Approximation of the two-dimensional Hubbard model. We investigate the energy spectrum of the two-dimensional Hubbard model, the numerator of the anticommutator Green's function. It should be noted that in the case of strong correlations, the ground-state energy of the antiferromagnetic phase is found to be lower than that of the paramagnetic phase.

The electron-spin resonance (ESR) of La_2-xSr_xCu_1-yFe_yO₄ is investigated on polycrystalline samples for 0 <= x <= 0.3 and 0 <= y <= 0.1. The ESR spectrum consists of the superposition of two Lorentzian lines, which can be unambiguously attributed to Fe³⁺ and intrinsic Cu-spin polaron signals. The simultaneous observation of both signals allows to describe the temperature dependence of the relaxation of the Fe³⁺ ions in terms of Cu-spin fluctuations.

New scenario of irreversibility for linear systems has been found and discussed. This scenario is based on the interpretation of the geometrical/physical meaning of the temporal fractional integral with complex and real fractional exponents. It has been shown that imaginary part of the fractional integral related to discrete-scale invariance (DSI) phenomenon and observed only for true regular (discrete) fractals. Numerical experiments show that the imaginary part of the complex fractional exponent can be well approximated by simple and finite combination of the leading sine/cosine log-periodical functions with period lnξ ( ξ is a scaling parameter). In the most cases analyzed the leading Fourier components give a pair of complex conjugated exponents defining the imaginary part of the complex fractional integral. For random fractals, where invariant scaling properties are realized only in the statistical sense the imaginary part of the complex exponent is averaged and the result is expressed in the form of the conventional Riemann-Liouville integral. The conditions for realization of reind and recaps elements with complex power-law exponents have been found. The fractal structures leading to pure log-periodic oscillations related to fractional integration with complex exponent are analyzed. Description of relaxation processes by kinetic equations containing complex fractional exponent and their possible recognition in the dielectric spectroscopy is discussed.

Four-layered FM/S/FM'/S' systems consisting of rather dirty superconducting (S) and ferromagnetic (FM) metals are sequentially considered on the basis of the original proximity effect theory early proposed for the artificial ferromagnetic metal/superconductor (FM/S) nanostructures. The dependences of critical temperatures on thicknesses of layers in a wide range of parameters are investigated. It is proved, this system can have different critical temperatures for layers S and S'. It is shown, that four-layered systems are the most perspective candidate for use in superconducting spin electronics and can serve element base for creation of the microelectronic equipment of essentially new type combining advantages of superconducting and magnetic record channels in one sample.

In the low doping range of x from 0.01 to 0.06 in La_2-xSr_xCuO₄ , we observed two electron paramagnetic resonance (EPR) signals: a narrow and a broad one. The narrow line is ascribed to metallic regions in the material, and its intensity increases exponentially upon cooling below  ~  150 K. The activation energy deduced ∆  = 460(50) K is nearly the same as that found in the doped superconducting regime by Raman and neutron scattering. Obtained results provide evidence of the microscopic phase separation and two type of quasiparticles in lightly doped La_2-xSr_xCuO₄.

On the basis of microscopic approach we derive the Eilenberger-type equations of superconductivity for metals with exchange-split conduction band. The equations are valid for arbitrary band splitting and arbitrary spin-dependent electron mean free paths within the quasiclassic approximation. Next, we deduce general boundary conditions for the above equations. These boundary conditions take into account explicitly spin-dependence of F/S interface transparency. We apply our theory for the Andreev reflection at F/S interface and derive an expression for the Andreev conductance at zero bias. Based on experimental data and our calculations we give estimations of the conduction band spin polarization for series of ferromagnets in contact with superconductors. Next, we consider the superconducting proximity effect for a contact of a strong and clean enough ferromagnet with a dirty superconductor. Our calculations show that superconducting T_c of an F/S bilayer oscillates as a function of the F-layer thickness. At small enough superconducting layer thickness the re-entrant behavior of superconductivity is predicted. The theory gives also nonmonotonic dependence of the superconducting layer critical thickness on the spin-polarization of the ferromagnetic layer. These unconventional and distinctive features of the F/S proximity effect fit well experimental observations.

Earlier obtained experimental data concerning sound propagation in silica aerogels filled in by liquid ⁴He are theoretically analyzed for normal as well as superfluid phase. The simple phenomenological model is proposed for normal phase. The data for superfluid phase are described in a rather good manner by the hydrodynamic theory with taking into account the clamping of normal component by silica strands. It is shown also that at temperatures below 1 K one needs a new hydrodynamic theory in which momentum transfer between aerogel and phonons in liquid helium should be taken into account

The complementary NMR and ESR studies of the frustrated phase separation in different superconducting cuprates are reported. We specially address the temperature dependence of the magnetic fluctuations and discuss their link with the observed superconducting state. It is argued that according to the phase diagram obtained for the lanthanum cuprates the superconducting phase coexists with the developed antiferromagnetic correlations. The observed picture is strongly dependent on the hole doping. In the vicinity of 1/8 doping such a coexistence may be realized in a form of dynamic stripes – the corresponding enhancement of the spin-stiffness reveals the plane character of the spin (and charge) inhomogeneities. Depending on whether these inhomogeneities are pinned or not, one has to distinguish the static and dynamical regimes of stripe fluctuations. With a help of our spin stiffness estimations, the upper threshold values of this quantity critical for the superconducting state were determined. The NMR analysis of the stripe phase local properties made it possible to estimate the local magnetic moment corresponding to antiferromagnetic domains as well as the charge of the domain walls.

The process of the high spin (HS)<-->low spin (LS) transition is studied in the polycrystalls of the Fe(III) thiosemicarbazonates, M[Fe(Th-R-Sa)₂], with M, R = Na, H (A); NH₄, 5-Br (B) and K, 5-Br (C) by the EPR method at atmospheric and hydrostatic pressure up to 600 MPa in the 80–400 K temperature range. The χ and  µ_eff were also measured for T =1.8–400 K. Spin transition (ST) in A is a continued one:  µ_eff changes from 5.9 µ_B at 330 K up to 5.7 µ_B at 50  K whereupon changes sharply to 3.4 µ_B at 1.8 K . The analysis of the EPR line width ∆B has shown its exchange origin. LS complexes (LSC) are not statistically distributed among the HS ones (HSC), but are gathered in a limited regions of structure – domains. The density of the LSC in domains increases with the T lowering. (∆B changes from ~ 70 – 80 mT at 200 K down to ~  20 mT at 80  K ). The line width ∆B sharply changes in the ST process at the two T intervals (240 – 236  K and 195 – 191  K ), pointing to the redistribution of the LSC in domains. Within 195 – 191 K this phenomenon is accompanied by the sharp increase of the LSC quantity.

The application of the external pressure P stimulates ST, however the character of the (HS)<-->(LS) process depends on T . At T>240 K LSC are not distributed accidentally, nevertheless their density at the regions of gathering is not high (∆>50 mT). The application of P below 236 K destroys domains partly, a number of the LSC returns to the HS state. The domains reorganization occurs at increasingly high P values at the T lowering.

ST takes place in B at the temperature interval 100 – 250 K (in interval 150–200 K it occurs more rapidly). It occurs through the domain formation as well but, contrary to the A case, the density of the LSC in domains grows very quickly. Already at the beginning of the EPR registration at P_atm  ∆(240  K )  ~  21 mT; ∆(170 K ) =~ 13.7 mT. In the T interval corresponding to the equal LSC and HSC contents, at T ~ 140 K, the abrupt transition from the separate existence of the LSC and HSC phases to their distributed state takes place. The pressure leads to the ST as well as the temperature does. About half of the complexes passes to the new spin state at P max  = 600 MPa. The state of the crystal is a transitional one at this P region. It shifts to the lower pressures at the temperature lowering. ST in C occurs in the 360 – 250 K T range. Its study allows to understand better the role of T and P at the ST process.

The processes of the domain formation and destruction show a definite hysteresis. The increase of the LSC density at the pre-domain state is defined by the pair correlations of the LS complexes. The cooperative effects lead to the sharp transformation of domains. The features of the self-regulation are inhered to the process of the transition of the crystal with the LS complex domains to the state equilibrium at given T and P .