Department for Astrophysics and Elementary Particles

- Observations with the Hubble Space Telescope have detected the radiation capable to ionize hydrogen, the most abundant element in the Universe, in five unique dwarf galaxies with active star formation and extremely high ionization degree of their interstellar medium. These galaxies were selected from the largest survey of Sloan sky. It is obtained for the first time that the fraction of this radiation ranges between 2% and 72% of the radiation produced in these galaxies. This fraction is sufficient to explain the secondary ionization of the early Universe at the stage when its age was between 200 and 800 million years. The indirect method is proposed which links the fraction of ionizing radiation escaping the galaxy with the profile of the bright Lyman-alpha emission line, the latter being more easily observed in distant galaxies. For this, the data were used for all 11 galaxies in the Local Universe observed with the Hubble Space Telescope. This method can be applied for galaxies at any distances including those at large distances, for which observations of ionizing radiation are difficult or impossible.
*Acad. of the NAS of Ukraine Y.I. Izotov, N.G. Guseva* - The term quadratic in curvature in the gravitational action in the Starobinsky model can be regarded as the leading quantum correction. We also assume the presence of parity-invariant and axial quantum corrections to the effective action that couple the space-time curvature to the electromagnetic strength tensor. We show that, in the Einstein frame of fields, there arises a nontrivial interaction between the scalar inflaton and electromagnetic field which previously was introduced in the theory artificially. Analysis of the inflationary magnetogenesis in this model shows that amplification of vacuum electromagnetic fields is possible no more than by five orders of magnitude, which is insufficient to explain the large-scale magnetic field in the Universe.
*Y. Shtanov, O. Savchenko* - We propose a characterization tool for the studies of the band structure of new materials promising for the observation of topological phase transitions. We show that a specific resonant feature in the entropy per electron dependence on the chemical potential may be considered as a fingerprint of the transition between topological and trivial insulator phases. The entropy per electron in a honeycomb two-dimensional crystal of germanene subjected to the external electric field is obtained from the first-principles calculation of the density of electronic states and the Maxwell relation. In a wide energy range, the van Hove singularities in the electronic density of states manifest themselves as zeros in the entropy per particle dependence on the chemical potential.
*Corr. Member of the NAS of Ukraine V.P. Gusynin, S.G. Sharapov*

Department for High-Density Energy Physics

- The equation of state with the induced surface tension is generalized to quantum gases with the mean-field interaction. Such an approach allows one to go beyond the Van der Waals approximation for quantum systems. Explicit expressions for the quantum virial coefficients of arbitrary order are found in the low density limit. All virial coefficients for the quantum Van der Waals equation of state are found as well.
*K.A. Bugaev, A.I. Ivanytskyi, V.V. Sagun, corresponding member of NAS of Ukraine G.M. Zinovjev* - The spectrum of photons with large transverse momentum is calculated and compared with the experimental data within the framework of the model of synchrotron radiation, which results from quark interactions with the collective confining color field in relativistic heavy ion collisions. It makes it possible to demonstrate the feasibility of this type of radiation due to distinctive features of lepton pair production in the corresponding experiments.
*Corr. Member of the NAS of Ukraine G.M. Zinovjev* - On the basis of Froissaron and Maximal Odderon model for proton and antiproton interaction at zero transferred momenta it is shown that the latest data of the TOTEM experiment at CERN give evidence for the discovery of odderon contribution, which was predicted almost 50 years ago. Moreover, the generalization of the model for differential cross-sections of nucleon elastic scattering confirmed the presence of odderon effects in the interaction of high-energy protons and antiprotons at non-zero transferred momenta.
*E.S. Martynov* - Statistical model of quark-gluon bags with a continuous transition to the high temperature phase is developed. Thermodynamical functions and fluctuations of conserved charges are calculated. The results are in agreement with those obtained within QCD lattice calculations.
*M.I. Gorenstein* - Within the framework of the evolution model of high ion collisions at LHC energies it is found that the inelastic reactions after matter hadronization influence on the relation of different particle number formation. Such reactions are important (compensated) factor of the hadron production, which restricts a direct studying the equation of quark-gluon plasma state and initial conditions of superdense matter formation.
*Yu.M. Sinyukov, V.M. Shapoval*

Department for Theory of Quantum Processes in Nanosystems

- A modified superexchange model for the formation of nonresonant tunnel current through a molecular wire consisting of a regular chain and terminal units is developed. Using the model, the dependence of current-voltage characteristics of alkanedithiol molecular wire on the number of C-C bonds are interpreted, and the conditions are formulated for which the simplest model of a rectangular barrier with a tunneling effective electron mass can be used for the analysis of experimental data.
*Corr. Member of the NAS of Ukraine E.G. Petrov* - A theory for the generation in a spheroidal metallic nanoparticle of an angular momentum under the action of ultrashort laser pulse is developed. New mechanism for generation of rotation force associated with nanoparticle polarization in the frequency region close to the surface plasmon resonances is proposed.
*N.I. Grigorchuk* - The nonequilibrium density matrix method for an open system coupled weakly to the environment is applied to consider the problem of maximizing performance of defected system via minimizing its sensibility to failures in an absorbing Markov chain framework. The objective is defined by maximizing competitiveness coefficient associated with the peak population of the failure-prone state with respect to increase in log input rate. It is shown that competitiveness coefficients calculated from simulations of brittle failures for three IR-transmitting window materials are in agreement with their performance derived from experiments.
*V.I. Teslenko, O.L. Kapitanchuk* - The influence of impurity atoms on the energy spectrum and the electrical conductivity of graphene is studied within one-band model of strong coupling. It is found out that the ordering of impurity atoms on the nodes of a crystal lattice leads to the appearance of a gap in the energy spectrum of graphene. It is shown that at some concentrations of impurities a metal-dielectric transition may occur, which leads to a strong increase in the electrical conductivity of graphene.
*S.P. Kruchinin* - The classic scheme of enzymatic catalysis is considered taking into account the nonlinear effects of substrate-conformation interaction. It is shown how the formation and interchange of the enzyme functional regimes is realized within the nonequilibrium phase transition scenario at the single molecule level.
*L.N. Christophorov*

Department for Mathematical Methods in Theoretical Physics

- Within the doubly special relativity theory which bounds both the velocities of particles (by the speed of light) and their energies (by the Planck scale) a new rule of so-called κ-addition for particle energies is proposed. A κ-dependent Hamiltonian of the one-mode multi-photon (sub)system is introduced and employed, with different modes being regarded as independent, to consider the thermodynamics of the black-body radiation and to obtain main thermodynamic quantities using analytical tools of the mean-field approximation and numerical evaluations based on exact formulas. The entropy of a one-mode subsystem turns out to be finite (bounded), and likewise the total energy density of radiation. Most unusual result is the existence of threshold temperature above which radiation is present.
*A.M. Gavrilik, A.V. Nazarenko* - A phenomenon of splitting (furcation) resonant tunneling under electron transmission through a plain layer in the form of a single delta-like barrier with at least one adjacent well located at non-zero sufficiently small distance has been observed. It is shown that in the zero-thickness limit of the heterostructure the detachment of a countable resonance curves from the background level occurs for certain critical value of the squeezing parameter.
*A.V. Zolotaryuk* - The Fredholm determinant and series representation of the tau-function of the Fuji-Suzuki-Tsuda system and its multivariate extension were derived. It is a generalization to higher rank (N=2) of the results obtained for Painlevé VI and the Garnier system. With its use a direct isomonodromic proof of the AGT-W relation for c=N−1 was obtained.
*N. Iorgov*

Department for Theory of Nonlinear Processes in Condensed Matter

- It is shown that inhomogeneous curvature of magnetic wire induces motion of a domain wall in the direction of the curvature gradient increasing. An asymptotic domain wall velocity is found. The resuts are verified by micromagnetic simulations.
*Yu.B. Gaididei, V.P. Kravchuk, K.V. Yershov* - The two-stage mechanism of the appearance of threshold deformations in a DNA macromolecule under the action of external force is proposed. At the first stage the appearance of a bistable state and the formation of domains with different conformations in the macromolecule chain occur for some critical value of external force. On the second stage the cooperative process of the domain walls propagation happens in the macromolecule. Thus, the emergence of bistability causes the threshold effect of deformation. The calculated parameters of the threshold elongation of DNA double helix are consistent with the experimental data.
*S.N. Volkov* - The character of hydration of Na
^{+}, K^{+}, Cs^{+}and Mg2^{+}counterions interacting with DNA double helix is studied using molecular dynamics simulations. The results show that structuring of the first and the second hydration shells of the ions is essential for the specific interactions with DNA. In particular, Na^{+}and Mg2^{+}interact with the DNA mostly via water molecules of the first hydration shell, while K^{+}and Cs^{+}may be dehydrated and penetrate deep into the minor groove of the double helix.*S.M. Perepelytsya* - It is shown that with the accuracy of the second order relativistic corrections the Hamiltonian of particles and antiparticles in an external field can be reduced to the Hamiltonian of non-interacting electrons and positrons. Operator invariants are obtained which describe spin states of relativistic particles. The Hamiltonian of electrons in the non-relativistic approximation is shown to contain both known and new relativistic corrections.
*A.A. Eremko, L.S. Brizhik, Acad. of the NAS of Ukraine V.M. Loktev* - Discrete time nonlinear quantum walk dynamics are studied. In the linear limit the spectrum of this model can be reduced to the complete flat band shape, what means the absence of transport and presence of the compact localized states. Existence of the soliton-like exitations that can propagate with constant velocity has been demonstrated. Due to the flatness of the linear spectrum the soliton does not resonate with it. The absence of the linear waves also causes the super-exponential [~exp(-exp(x))] decay of the soliton amplitude.
*Ya. Zolotaryuk* - The new nonlinear integrable system of classical intra-molecular excitations on a ladder lattice with three structural elements in the unit cell is suggested. The Poisson structure and the Hamiltonian formulation of the system are found. In the framework of Darboux transformation for an auxiliary spectral problem the system’s multicomponent soliton solution is obtained.
*O.O. Vakhnenko*

Department for Synergetics

- In terms of the nonequilibrium statistical operator, the fundamental scalar field is shown to provide a natural representation of the repulsive interaction that produces scattering in the system and thus motivates law of entropy increasing.
*Corr. Member of the NAS of Ukraine B.I. Lev* - It is proposed a model of the first-order phase transition in the liquid crystals on the graphene surface with impurities which can change the orientation conditions. Experiments which confirm the theoretical predictions are performed out.
*Corr. Member of the NAS of Ukraine B.I. Lev* - Noncongruent first-order liquid-gas phase transition is studied within the quantum van der Waals model with two chemical potentials which regulate two conserved charges.
*M.I. Gorenstein, R.V. Poberezhnyuk* - Taking an excitatory neuron with delayed feedback as an example it is proven that statistics of activity of a neuron with such a feedback cannot be presented as Poisson process.
*O.V. Shchur, A.K. Vidybida* - Calculation of electromagnetic field energy in a medium with temporal and spatial dispersion outside thetransparency domain is discussed. It is shown that charged particle contribution to the energy of electromagnetic perturbations in the general case can be described in terms of a bilinear combination of the dielectric polarizability of the medium. The explicit form of such contribution is found. The relations obtained are used to generalize the Planck law and Kirchhoff law to the case of an absorptive medium with spatial dispersion.
*Acad. of the NAS of Ukraine A.G. Zagorodny* - On the basis of microscopic approach consistent kinetic theory is formulated for low temperature dilute gases of hydrogen-like atoms in an external electromagnetic field. Within the proposed approach the set of kinetic equations for Wigner distribution functions is obtained for free fermions of both sorts and their bound states — hydrogen-like atoms with regard to the influence of external and self-consistent (mean) fields.
*Acad. Of the NAS of Ukraine A.G. Zagorodny* - The dispersion relation for ion-acoustic waves in collisional weakly ionized dusty (complex) plasma is formulated with due regard to the grain charge fluctuations. The dependencies of the charging frequencies and effective collision frequencies on dusty plasma parameters are studied in detail. The analysis of the ionacoustic wave spectrum is presented for the wide range of the ion collisionality for both nonisothermal and isothermal plasmas.
*Acad. Of the NAS of Ukraine A.G.Zagorodny* - On the basis of the developed analytical method, the dependence of the magnetized plasma particle transverse diffusion coefficient on the correlation time of random electric fields is obtained. The results of calculations are in agreement with the data of numerical simulation in a wide range of correlation times.
*V.I. Zasenko, O.M. Chernyak* - It is proved that a risky asset, which evolves according to the law of discrete geometric Brownian motion, in contrast to the continuous case generates an incomplete financial market. New convenient research formula for a fair price of super-hedge for a broad class of payment functions is found.
*N.S. Gonchar* - The internal factors that form the exchange rate “hryvnia/dollar” are established, and proposals are made regarding the macroeconomic policy of the state to stabilize inflation.
*N.S. Gonchar, V.H. Kozyrsky, A.S. Zhokhin, O.P. Dovzhyk* - A mathematical model of the kinetics of a polyenzyme biosystem with nonstationary kinetics of a strange attractor was constructed.
*A.S. Zhokhin* - It has been demonstrated that the electron-vibron interaction and the local pairing of electrons on the 3-fold degenerate molecular orbital causes superconductivity of alkali-doped fullerides which would have to be antiferromagnetic Mott insulators.
*K.V. Grigorishin*

Department for Theory of Nuclei and Quantum Field Theory

- The continuum model for long-wavelength charge carriers, originating in the tight-binding approximation for the nearest-neighbour interaction of atoms in the crystalline lattice, is applied to consider quantum ground-state effects of electronic excitations in Dirac materials with two-dimensional monolayer honeycomb structures warped into nanocones by a disclination. The magnetic flux circulating in the angular direction around the nanocone apex and the pseudomagnetic flux directed orthogonally to the nanocone surface are shown to be induced in the ground state.
*Corr. Member of the NAS of Ukraine Yu.A. Sitenko* - New analytical expressions for the three-dimensional Coulomb matrix of transition are derived for energies corresponding to the integral and semi-integer value of the Sommerfeld parameter.
*V.F. Kharchenko* - Within the framework of a nonperturbative quantum theory of gravitation, based on the quantum generalization of the Hamilton-Jacobi equation of general relativity, it is shown that during the evolution of the early universe the cosmological parameters, i.e., the matter-energy density, the pressure, and the deceleration parameter, may fluctuate between positive and negative values under the influence of quantum corrections to the energy density.
*V.E. Kuzmichev* - Simple relations connecting the strange s-quark mass to the splittings of the light hyperon masses are obtained on the basis of the phenomenological quark model compatible with the quantum chromodynamics (QCD). The value of strange s-quark mass, calculated in the proposed approach, is in good agreement with the modern evaluations and calculations of this quantity, obtained by the lattice QCD methods.
*V.A. Babenko, N.M. Petrov* - An alternative way of light nuclei synthesis in the stellar environment through a triple collision of nuclei and the excitation of a narrow resonance state is studied in detail. It is shown that the long-lived resonance state which is a key element of synthesis of carbon ‒ the Hoyle-analog state ‒ exists also in the light nuclei
^{9}Be,^{9}B,^{11}B and^{11}C. Such resonance states are generated by collisions of two alpha-particles with neutrons, protons, tritons, and nuclei^{3}He, respectively. The Hoyle-analog states are not observed in the nucleus^{10}B consisting of two alpha-particles and a deuteron.*V.S. Vasilevsky, Y.A. Lashko, G.F. Filippov* - Structure characteristics of the lowest excited state of the mirror nuclei
^{14}С and^{14}О are studied within a five-particle model (three α-particles plus two extra nucleons) in terms of the variational approach with the Gaussian bases. The charge radius of^{14}О is calculated, and it is explained why this radius is smaller than that of^{14}С nucleus, although^{14}О contains two extra protons instead of two extra neutrons in^{14}С. Both elastic and transition electrical form-factors of^{14}C and^{14}O nuclei are calculated.*V. S. Vasilevsky, B. E. Grinyuk, D. V. Piatnytskyi* - Within the discrete representation of the harmonic oscillator basis, eigenvalues and eigenfunctions of the potential energy matrix are investigated for a particle in the field of central spherical square-well potentials, Gaussian potential, Yukawa potential and exponential potential. For all the potentials considered, the eigenfunctions of the potential energy operator in the discrete representation are shown to be harmonic oscillator basis functions. In the momentum representation the eigenfunctions of the potential energy operator are proved to be spherical Bessel functions.
*Y.A. Lashko*