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It has been shown that interband mixing of gradients of two order parameters (drag effect) in an isotropic bulk two-band superconductor plays important role -such a quantity of the intergradients coupling exists that the two-band superconductor is characterized with a single coherence length and a single Ginzburg-Landau (GL) parameter. Other quantities or neglecting of the drag effect lead to existence of two coherence lengths and dynamical instability due to violation of the phase relations between the order parameters. Thus so-called type-1.5 superconductors are impossible. An approximate method for solving of set of GL equations for a multi-band superconductor has been developed: using the result about the drag effect it has been shown that the free-energy functional for a multi-band superconductor can be reduced to the GL functional for an effective single-band superconductor.

Generalization of a disordered metal's theory has been proposed when scattering of quasiparticles by impurities is caused with a retarded interaction. It was shown that in this case Anderson's theorem was violated in the sense that embedding of the impurities in s-wave superconductor increases its critical temperature. The increasing depends on parameters of the metal, impurities and their concentration. At a specific relation between the parameters the critical temperature of the dirty superconductor can essentially exceed critical temperature of pure one up to room temperature. Thus the impurities catalyze superconductivity in an originally low-temperature superconductor.

Based on statistical approach we described possible formation of spatially inhomogeneous distribution in the system of interacting Bose particles. The condition of cluster formation in both gas and condensed phases was obtained in this system. We studied the dynamics of cluster formation in the limit case of high temperatures. We compared the cluster-formation processes in the attractive system (with short-range interaction) and in the gravitational system at the low temperatures of Bose-Einstein condensate regime.

b Metrolohichna str. Kiev-03680, Ukraine.We investigate the competition between the electron-vibron interaction (interaction with the Jahn-Teller phonons) and the Coulomb repulsion in a system with the local pairing of electrons on the 3-fold degenerate lowest unoccupied molecular orbital (LUMO). The el.-vib. interaction and the local pairing radically change conductivity and magnetic properties of alkali-doped fullerides AnC60, which would have to be antiferromagnetic Mott insulators: we have shown that materials with n = 1, 5 and A = K, Rb are conductors but not superconductors; n = 3 and A = K, Rb are conductors and superconductors at low temperatures, but with A = Cs they are Mott-Jahn-Teller insulators at normal pressure; n = 2, 4 are nonmagnetic Mott insulators. Thus superconductivity, conductivity and insulation of these materials have common nature. Using this approach we obtain the phase diagram of A3C60 analytically, which is the result of interplay between the local pairing, the el.-vib. interaction, Coulomb correlations, and formation of small radius polarons.

The model of hypothetical superconductivity, where the energy gap asymptotically approaches zero as temperature or magnetic field increases, has been proposed. Formally the critical temperature and the second critical field for such a superconductor is equal to infinity. Thus the material is in superconducting state always. PACS numbers: 74.20.Fg, 74.20.Mn Critical temperature T C and critical magnetic fields H c , H c2 are most important characteristics of a superconductor. The critical parameters depends on an effective coupling constant with some collective excitations g = ν F λ 1 (here ν F is a density of states at Fermi level, λ is an interaction constant), on frequency of the collective excitations ω and on correlation length ξ 0 . The larger coupling constant, the larger these critical parameters. For example, for large values of g we have T C ∝ ω √ g [1, 2] (or T C ∝ ωg in BCS theory). Formally the critical temperature can be made arbitrarily large by increasing the electron-phonon coupling constant. However in order to reach room temperature such values of the coupling constant are necessary which are not possible in real materials. Moreover we can increase the frequency ω due nonphonon pairing mechanisms as proposed in [2]. However with increasing of the frequency the coupling constant decreases as g ∝ 1/ω, therefore T C (ω → ∞) = 1.14ω exp (−1/g) → 0. The second critical magnetic field can be enlarge due to the decrease of the correlation length in "dirty limit, where l is a free length. However the critical field is low near the critical temperature: H c2 (T → T C ) → 0. In a present work we generalize BCS model so that the problem of the critical parameters is removed due to the fact that a ratio between the gap and the critical temperature (2∆/T C = 3 ÷ 7 for presently known materials) is changed to 2∆/T C → 0. We consider a system of fermions with Hamiltonian:where H BCS is BCS Hamiltonian -kinetic energy + pairing interaction ( which are the complex order parameter ∆ = |∆|e iθ . The multipliers ∆ |∆| and ∆ + |∆| are introduced into H ext in order that the energy does not depend on the phase θ (a → ae iθ/2 , a

We propose a perturbation theory and diagram technique for a disordered metal when scattering of quasiparticles by nonmagnetic impurities is caused with a retarded interaction. The perturbation theory generalizes a case of elastic scattering in a disordered metal. Eliashberg equations for s-wave superconductivity are generalized for such a disordered superconductor. Andersonʼs theorem is found to be violated in the sense that embedding of the impurities into an s-wave superconductor increases its critical temperature. We show that the amplification of superconducting properties is a result of nonelastic effects in a scattering by the impurities.

-b Metrolohichna str. Kiev-03680, Ukraine.We consider a hypothetical substance, where interaction between (within) structural elements of condensed matter (molecules, nanoparticles, clusters, layers, wires etc.) depends on state of Cooper pairs: an additional work must be made against this interaction to break a pair. Such a system can be described by BCS Hamiltonian with the external pair potential term. In this model the potential essentially renormalizes the order parameter: if the pairing lowers energy of the structure the energy gap is slightly enlarged at zero temperature and asymptotically tends to zero as temperature rises. Thus the critical temperature of such a superconductor is equal to infinity formally. For this case the effective Ginzburg-Landau theory is formulated, where the coherence length decreases as temperature rises, the GL parameter and the second critical field are increasing functions of temperature unlike the standard theory. If the pairing enlarges energy of the structure then suppression of superconductivity and the first order phase transition occur.