Department for Astrophysics and Elementary Particles

- The electron states in the field of a charged impurity in graphene in a magnetic field are studied. It is shown that a charged impurity removes the degeneracy of Landau levels converting them into bandlike structures. As the charge of impurity grows, the repulsion of sublevels of different Landau levels with the same value of orbital momentum takes place leading to the redistribution of the wave function profiles of these sublevels near the impurity. By studying the polarization effects, it is shown that the filling of Landau levels and screened charge of impurity can be very effectively tuned by gate voltage in agreement with the recent experiments. If the chemical potential is situated inside a Landau level, then the charge of impurity is strongly diminished. If the chemical potential lies between the Landau levels, then the screened potential does not change sign, the screening is minimal, and the charged impurity can strongly affect the electron spectrum.
*E.V. Gorbar, V.P. Gusynin* - Sterile neutrino with mass of about 7 keV can explain the properties of the emission line at energy ~3.5 keV in the spectra of several dark-matter dominated cosmic objects. We investigate the influence of dark matter composed of such sterile neutrino on the process of reionization of the Universe and show that it causes a significantly sharper reionization, impossible to `imitate' within the cold-dark-matter scenario under any reasonable choice of model parameters. The future dedicated studies of reionization by 21-cm tomography of the Universe and investigations of the kinetic Sunyaev-Zeldovich effect will become essential for the reconstruction of particle candidate responsible for the 3.5 keV emission line.
*A. Rudakovskyi, D. Iakubovskyi* - The process of generation and subsequent free evolution of the lepton chiral asymmetry and helical magnetic field in the early hot universe is studied analytically. For cosmologically relevant initial conditions, the chiral asymmetry and the energy density of helical magnetic field are shown to evolve by scaling laws. We derived an expression for the temperature at which this regime abruptly terminates as a function of the chiral asymmetry and energy density of magnetic field.
*M.Ye. Sydorenko, Y.V. Shtanov*

Department for High-Density Energy Physics

- A novel formulation of lattice SU(2) gluodynamics in terms of geometrical clusters of two types formed by the Polyakov loops was developed and the equivalent thermodynamic description of lattice gluodynamics in the vicinity of deconfinement phase transition was obtained. For the first time the temperature dependence of physical surface tension of geometrical clusters is found directly from the lattice QCD. It is also found that the surface tension of these clusters can be used as a new order parameter for the corresponding phase transition.
*K.A. Bugaev, A.I. Ivanytskyi, V.V. Sagun, D.R. Oliinychenko, G.M. Zinovjev* - An extension of the hadron resonance gas model which includes the attractive and repulsive van der Waals interactions between baryons is constructed. This model yields the nuclear liquid-gas 1st order phase transition at low temperatures and high baryon densities. A behavior of fluctuations and correlations of baryon number, electric charge, and strangeness in the so-called crossover region T = (140–190) MeV resembles closely the results obtained from lattice QCD simulations.
*M.I. Gorenstein* - Analysing two models of four-quark (Nambu-Jona-Lasinio model and Keldysh model) interactions which are of intrinsic difference in the behaviors of their correlation lengths some issues of quark condensations are considered. It is demonstrated that the quark condensates substantially are not sensitive to the details of those interactions in the range of coupling constants interesting for applications.
*G.M. Zinovjev* - Within the integrated hydrokinetic model, it is analyzed the transverse momentum pT-dependence of the pair correlations of strange mesons and baryons that are created in nucleus-nucleus collisions at Large Hadron Collider (LHC) and Relativistic Heavy Ion Collider (RHIC). By using the correlation functions for different pair species (kaon-kaon, Lambda-proton, Cascade – proton), the femtoscopic spatiotemporal picture of the pairs emission is restored. At that, the pT –scaling behavior of kaon and pion femto-scales is revealed. The result is confirmed now in the experiments at RHIC and LHC.
*Yu.M. Sinyukov, V.M. Shapoval*

Department for Theory of Quantum Processes in Nanosystems

- It is shown that in a molecular diode, one can observe a specific unipolar electrofluorescence which differs strongly from the electrofluorescence associated with the Stark shift of the levels. The origin of the noted electroluminescence is that the coupling of the molecular chromophore group to one electrode is much stronger the coupling to another electrode. This brings to the strongly asymmetric population of an excited molecular state at identical in value but different in sign of the voltage bias. The critical voltages that change the regimes of electron transmission, are found and the conditions to observe the unipolarity are formulated.
*E.G. Petrov, V.O. Leonov, Ye.V. Shevchenko* - The decay mechanism for plasmon is proposed through the photon irradiation by electron scattering from surface of the metallic particles with a spheroidal form surfaces, embedded in some dielectric matrix. It allows one both to evaluate the linewidth of surface plasmon in metallic nanoparticle directly through the tensor of optical conductivity and to establish it dependence on the particle radius and medium refractive index.
*M.I. Grigorchuk* - Spin-dependent transport investigated in carbon nanotubes with chromium atoms. Precise expressions for Green’s functions, thermodynamic potential and conductivity tensor are derived using diagram method. We show that the phenomenon of spin-dependent electron transport in a carbon nanotube was the result of strong electron correlations, caused by the presence of chromium atoms. The value of the electric current spin polarization increases along with Cr atoms concentration and magnitude of the external magnetic field increase.
*S.P. Kruchinin* - Energy spectra, ionization potentials, electron affinity and reorganizations energies were calculated within density functional theory approach for the series of ter-anthrylene-ethynylene derivatives being in neutral, cationic and anionic charge states. The oscillating behavior of intramolecular transfer integral values was observed both for electron and hole charge carriers, hole mobility was predicted to be higher than electron one.
*O.L. Kapitanchuk* - A three-stage kinetic model for the blockage of calcium channels by nickel ions in biological membranes is introduced. In correspondence to the experiment it is established that the peak calcium-current magnitudes comprise the hysteresis property and obey bimodal distributions over the logarithm of the antagonist’s concentrations.
*V.I. Teslenko, E.G. Petrov* - Peculiarities of migration and capture of a quantum particle in the chain with traps are described. Nontrivial dependencies of the quantum yield of capture W(χ) on the trap intensity χ (in particular, the effect of 'imprisonment' of the particle in the chain with χ growing) and initial conditions of migration are revealed in the cases of infinite, semi-infinite and finite chains.
*L.N. Christophorov, A.G. Zagorodny*

Department for Mathematical Methods in Theoretical Physics

- Ideal D-dimensional Bose gas is considered in a trap (external potential) in more general case than in previous works, namely, for isotropic potential
*U(r) = Ar*, where^{n}+Br^{-m}*A, B*> 0. The momentum distribution function is obtained, as well as the total number of particles, critical temperature, condensate fraction and heat capacity. Both high and low temperature regimes are considered. Conditions for the existence of Bose-Einstein condensation in the form of certain relations on*n*,*m*and*D*are being obtained.*A.M. Gavrilik, I.I. Kachurik, Yu.A. Mishchenko* - The whole class of one-point interactions realized in the limit when the thickness of two- and three-layer planar heteostructures as well as the distance between them are infinitesimal. It is established that depending on the way of realization of this limit, in the tunneling of electrons, the phenomenon of furcation of isolated resonances into multi-valued sets takes place.
*A.V. Zolotaryuk* - We study symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are considered to be fixed different. The probability to find a walker at the given position and time is derived analytically. The probability distribution function is found: it has non-Gaussian form because of the properties of adsorption in the bulk of zones and reflection at the separation points. Time dependence of the mean squared displacement of a walker is also studied, and the anomalous behavior is revealed as compared with ordinary RW. Analytical calculation is in agreement with the results of numerical modeling based on first principles.
*A.V. Nazarenko*

Department for Theory of Nonlinear Processes in Condensed Matter

- It is known that the Shubnikov - de Haas oscillations can be observed in the Hall resistivity, although their amplitude is much weaker than the amplitude of the diagonal resistivity oscillations. Employing a model of two-dimensional massive Dirac fermions that exhibits anomalous Hall effect, we demonstrate the amplitude of the Shubnikov - de Haas oscillations of the anomalous Hall conductivity is the same as that of the diagonal conductivity. We argue that the oscillations of the anomalous Hall conductivity can be observed by studying the valley Hall effect in graphene superlattices and the spin Hall effect in the low-buckled Dirac materials.
*S.G. Sharapov* - It is shown that the curvature and torsion of a ferromagnetic nanowire significantly affect the spin-polarized current induced domain wall motion along the wire. We consider the simplest case of constant curvature and torsion, corresponding nanowires in the form of three-dimensional helix. It is shown that the curvature leads to Walker breakdown, i.e. the emergence of a critical density of spin-polarized current j
_{c}, which separates two modes of motion: translational motion when j<jc and oscillating motion for j> j_{c}. In the point j = j_{c}a saddle-node bifurcation takes place. The nanowire torsion, in turn, leads to a shift of the material parameter of spin torque nonadiabaticity. The shift is proportional to the product of the helix chirality to the topological charge of the domain walls. This shift can be negative, that can lead to negative domain wall mobility. Basing on the obtained results we propose a practical method of experimental measurement of the nonadiabaticity parameter and the damping coefficient.*Yu.B. Gaididei, V.P. Kravchuk, K.V. Yershov* - The analytical expression for the spectrum of electrons in quasi-two-dimensional space (so called 2D electrons) is found within the fundamental Dirac equation. Such system describes layered heterostructures, interfaces, crystal surfaces, etc. It is shown that the exact solution contains several spin invariants, which means possibility of the existence of many spin states of quasi-2D electrons with different spin polarization and different effects of spin-orbit interaction on the energy spectrum. The exact solution is found for electrons confined by asymmetric potential well, which includes free parameters, whose value corresponds to certain invariants. In the general case the spin quantum number determines certain value of the linear combination of all invariants. These results allow to ascertain the conditions at which the given spin state is realized, which opens new perspectives to control the spin degree of freedom of charge carriers in spintronics.
*A.A. Eremko, V.M. Loktev, L.S. Brizhik* - We present the analytic analysis of the spectral problem for bounded graphene fragments and finite polyene chains. The solutions of the transcendental equation for the characteristic quantum numbers are thoroughly examined and their accurate approximations are proposed. The obtained results are used for analysis of the fundamental and technologically significant properties of graphene and its daughter structures (i.e., zigzag and armchair graphene nanoribbons), and finite polyene chains of various length.
*L.I. Malysheva* - The variativity of governing coupling parameters in the integrable nonlinear Schrödinger system on a triangular-lattice ribbon is shown to ensure the important qualitative rearrangements in the system dynamics. Thus the longitudinal coupling parameters regulated mainly by the background values of concomitant field variables are responsible for the bifurcation of primary integrable nonlinear system into the integrable nonlinear system of Ablowitz-Ladik type. As a consequence in a critical point the number of independent field variables is reduced by a half and the system Poisson structure turns out to be degenerate. On the other hand the transverse coupling parameters regulated basically by the choice of their a priori arbitrary dependencies on time are capable to incorporate the effect of external linear potential. As a consequence the primary integrable nonlinear system with appropriately adjusted parametrical driving becomes isomorphic to the system modelling the Bloch oscillations of charged nonlinear carriers in an electrically biased ribbon of triangular lattice.
*O.O. Vakhnenko* - Molecular force field (CHARM), which is commonly used in computer simulations to study the structure and dynamics of macromolecules in biological systems, is modified. A new type of potential function allows us to study the processes of chemical bonds breaks, the rupture of valence angles and dihedral interactions in molecules. Modified force field implemented in the software package MBN Explorer.
*S.N. Volkov* - The structure functions of the mirror nuclei 14С and 14O are studied within a model "three alpha-particles plus two extra nucleons". The charge density distributions, form factors, pair correlation functions, and the momentum distributions of particles are found for these nuclei. Two spatial configurations are revealed in the ground state of 14С and 14O nuclei. The unknown experimental charge r.m.s. radius of 14O nucleus is predicted.
*B.E. Grinyuk, D.V. Piatnytskyi*

Department for Synergetics

- 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.
*K.V. Grigorishin* - A general concept of the long-range elastic interactions in continuous medium is proposed. The interaction is determined as a consequence of symmetry breaking of the elastic field distribution produced by the topological defect as isolated inclusions. It is proposed to treat topological defects as the source of elastic field that can be described in terms of this field. The source is considered as a nonlinear object which determines the effective charge of the field at large distances in the linear theory. The models of the nonlinear source are proposed.
*A.G. Zagorodny, B.I. Lev* - We have introduced the elliptic-beam model for the transmittance probability distribution (PDT) of the atmospheric quantum channel. This model adequately accounts the loss and fading of the signal due to the atmospheric distortions of the beam centroid position and beam deformation. It appears that our model applies to weak, weak-to-moderate, and strong turbulence and hence to the most important regimes in atmospheric communication scenarios (PRL,117, 090501б (2016)). As an example we have studied the influence of atmospheric turbulence on quantum nonlocality for the scenario of counterpropagation of photonic pair as well as the influence so-called double-click events, which are caused by dark counts, stray light, and multiphoton entangled pairs.
*D.Yu. Vasyljev* - Method of preparation of multimode sub-Poisson light was developed using control photodetection of multimode twin-beam squeezed vacuum states and imposing a condition on the main photodetector. The method was shown useful upon imperfect detection efficiency. The numerical modeling was carried out followed by the experimental verification of the method for bright nonclassical light in collaboration with Max-Planck Institute for the Science of Light in Erlangen.
*V.C. Usenko* - The size of air bubbles in nematic liquid crystals can be continuously decreased through the absorption of air molecules into the host liquid crystal. A bubble and its accompanying hyperbolic hedgehog point defect undergo a continuous asymmetric motion, while the bubble decreases in size. In this study, a mechanism is proposed to theoretically explain both the motion of the air bubble and the point defect observed experimentally. Anisotropic evaporation of air molecules may occur because of the symmetry breaking of the director configuration near the point defect. The motion of the center of the air bubble to the hyperbolic hedgehog point defect is induced by the anisotropic force due to evaporation of air molecules and Stokes drag force.
*B.I. Lev* - For leaky integrate-and-fire neuron with threshold 2 stimulated with Poisson stream, intensity of the output stochastic process is calculated without using the diffusion approximation as function of LIF's physical parameters and intensity of the input stochastic process.
*О.К. Vidybida* - Within a mathematical model, the process of interaction of the metabolic processes such as glycolysis and gluconeogenesis is studied. As a result of the running of two opposite processes in a cell, the conditions for their interaction and the self-organization in a single dissipative system are created. The reasons for the appearance of autocatalysis in the given system and autocatalytic oscillations are studied. With the help of a phase-parametric diagram, the scenario of their appearance is analyzed. The bifurcations of the doubling of a period and the transition to chaotic oscillations according to the Feigenbaum scenario and the intermittence are determined. The obtained strange attractors are created as a result of the formation of a mixing funnel. Their complete spectra of Lyapunov indices, KS-entropies, ―horizons of predictability,‖ and the Lyapunov dimensions of strange attractors are calculated. The conclusions about the reasons for variations of the cyclicity in the given metabolic process, its stability, and the physiological state of a cell are made.
*V.I. Grytsay* - We uncovered physical underpinnings of formation of colloidal elastic hexadecapoles and described the ensuing bonding inaccessible to elastic dipoles, quadrupoles and other nematic colloids studied previously.
*S.B. Tovkach* - Peculiarities of migration and capture of a quantum particle in the chain with traps are described. Nontrivial dependencies of the quantum yield of capture W(χ) on the trap intensity χ (in particular, the effect of 'imprisonment' of the particle in the chain with χ growing) and initial conditions of migration are revealed in the cases of infinite, semi-infinite and finite chains.
*L.N. Christophorov, A.G. Zagorodny* - The analytical approach for description of magnetized particle transport in random frozen isotropic electrostatic field is developed using the concept of subensembles. It is shown that more detailed description in terms of subensembles gives better quantitative agreement with results of direct numerical simulation.
*V.I. Zasenko, O.М Cherniak, A.G. Zagorodny* - The electrostatic potential distribution around a solitary charged absorbing macroparticle embedded into weakly ionized strongly collisional plasma is studied in details on the bases of numerical solutions of plasma dynamic nonlinear equations within the drift-diffusion approximation. Calculation was done under assumption that a macroparticle absorbs electrons and ions from plasma environment; the dependence of accumulated charge on dust particle size as well as plasma parameters is found. The comparison of calculated potential and plasma particles distributions with analytical expressions is performed. It is shown that consistency of analytic approximations (the superposition of Debye and Coulomb potentials) with the results of calculations can be significantly improved by use of a screening length scaling which depends on a dusty particle size and is associated with a significant deviation of a charge density near the particle surface from the unperturbed value. The universal dependence of the scaling parameter for screening length and effective charges on macroparticle size is obtained.
*A.G. Zagorodny, A.I. Momot* - Mathematical model of rate of exchange and targeting inflation is constructed. Stochastic difference equation for the rate of exchange hryvnia/dollar is established. An equation of money circulation that relate money demand, nominal Gross National Product, rate of National Bank, price level is constructed. Money circulation velocity during 2012-2014 ages is found and it is proved that it grows. This fact certifies inflation growing in this period and falling of living standard.
*N.S. Gonchar, A.S. Zhokhin, W.H. Kozyrski, L.S. Terentieva* - A notion of local regular supermartingale relative to a convex set of equivalent measures is introduced. The theorem giving the necessary and sufficient conditions of validity of optional decomposition for local regular supermartingales is proved that is generalization of the well known Doob decomposition theorem for supermartingale. Complete description of local regular supermartingales relative to a convex set of equivalent measures is given. An important notion of complete convex set of equivalent measures is introduced and theorem stating that for all non negative supermartingale relative to this set of measures optional decomposition is valid. This result is important for Mathematical Finance. Fair price for contingent claim relative to a convex set of equivalent measures is introduced that is generalization of the notion in case as the set of equivalent measures is a set of equivalent martingale measures for a certain evolution of risk and non risk assets. A formula for fair price of standard contract with European option for arbitrary non arbitrage evolution as risk and non risk assets in incomplete market is found.
*N.S. Gonchar*

Department for Theory of Nuclei and Quantum Field Theory

- We study the influence of boundaries on chiral effects in hot dense relativistic spinor matter in a strong magnetic field which is orthogonal to the boundaries. It is shown that the chiral magnetic effect disappears, whereas the chiral separation effect becomes dependent not only on chemical potential, but on temperature and on a boundary condition as well. These points at a significant role of boundaries for physical systems with hot dense magnetized spinor matter, i.e. compact astrophysical objects (neutron stars and magnetars), relativistic heavy-ion collisions, novel materials known as the Dirac and Weyl semimetals.
*Yu.A. Sitenko* - New approach to the description of the off-shell Coulomb scattering amplitude that is based on using the Fock’s method of the stereographic projection of the momentum space onto the four-dimensional unit sphere has been worked out. New analytical expressions for the partial-wave off-shell Coulomb transition matrices for particles with the repulsive interaction at the ground-state energy have been derived.
*V.F. Kharchenko* - Charge independence breaking (CIB) in the pion-nucleon coupling constant and the nucleon-nucleon scattering length is considered on the basis of the Yukawa meson theory. The CIB effect in these quantities is almost entirely explained by the mass difference between the charged and the neutral pions. Therewith charge splitting of the pion-nucleon coupling constant is almost the same as charge splitting of the pion mass.
*V.A. Babenko, N.M. Petrov* - The structure functions of the mirror nuclei
^{14}С and^{14}O are studied within a model "three alpha-particles plus two extra nucleons". The charge density distributions, form factors, pair correlation functions, and the momentum distributions of particles are found for these nuclei. Two spatial configurations are revealed in the ground state of^{14}С and^{14}O nuclei. The unknown experimental charge r.m.s. radius of^{14}O nucleus is predicted.*B.E. Grinyuk, D.V. Piatnytskyi* - Theoretical analysis of bound and resonance states in
^{10}Be nucleus is performed within a microscopic three-cluster model. This nucleus is represented as three-cluster system comprised of two alpha particles and a dineutron. The latter is two neutrons correlated in the space, which form a pseudo-bound state. The processes of elastic and inelastic scattering of alpha particles from^{6}He and dineutron from^{ 8}Be are also investigated. Within the present model, nuclei^{6}Не and^{8}Ве are considered as two-cluster systems, which consist of alpha particle and dineutron and two alpha particles, respectively. One of main aims of the present investigation is to study how cluster polarization of nuclei^{6}Не and^{8}Ве affects the structure of bound and resonance states in^{10}Ве and elastic and inelastic processes as well. It is shown that nuclei^{6}Не and^{8}Ве are substantially changed their size and shape when they interact with alpha particle and dineutron, respectively. It is also shown that the cluster polarization strongly changes a mutual attraction of clusters in the compound system and leads to larger energy of bound states and smaller energy and width of resonance states of the three-cluster system. Within the present model, we obtain good agreement of theoretical results with available experimental data for discrete and continuous spectrum states in^{10}Ве.*Yu.A. Lashko, G.F. Filippov, V.S. Vasilevsky*