Department for Astrophysics and Elementary Particles

- The electron states of gapped pseudospin-1 fermions on a honeycomb lattice with additional atoms in the center of each hexagon (dice lattice) were studied in the presence of a charged impurity. The bound electron states are found in the case of the radially symmetric potential well and a regularized Coulomb potential. It is shown that as the charge of the impurity increases, bound-state energy levels descend from the upper and central continua and dive at certain critical charges into the central and lower continua, respectively, realizing the so-called phenomenon of atomic collapse for pseudospin-1 fermions. In the dice model, it is found that the flat band survives in the presence of a potential well, however, it is absent in the case of the Coulomb potential. The analytical results were obtained for the energy levels near continuum boundaries in the potential well. For the genuine Coulomb potential it is shown that analytical solutions exist for a countably infinite set of values of impurity charge at fixed couplings of atoms.
*Corr. Member of the NAS of Ukraine V.P. Gusynin, E.V. Gorbar* - A method to describe the electric field in a spontaneously polarized isotropic nonpolar dielectric is developed. Helmholtz formula for the electric force acting on a volume element of a dielectric is generalized with regard for the contribution of the spontaneous polarization.
*M.D. Tomchenko* - Observations with the Hubble Space Telescope of eight compact star-forming galaxies, aiming to study the properties of Lyman-alpha emission in such conditions, have been presented. The relation between the Lyman-alpha escape fraction and the Lyman-continuum escape fraction has been examined. It was found that shape the Lyman-alpha is a good measure of the escaping Lyman-continuum radiation and can be applied for a large number of the galaxies aiming to solve the problem of the reionization of the Universe.
*Acad. of the NAS of Ukraine Y.I. Izotov, N.G. Guseva* - A simple scenario of inflationary magnetogenesis is proposed based on a helical coupling to electromagnetism. The helical coupling evolves linearly with conformal time interpolating between two constant values. This allows one to avoid the problem of strong gauge coupling and to generate helical magnetic fields of strength of order up to 10
^{–7}G, when extrapolated to the current epoch, in a narrow spectral band centered at any physical wavenumber by adjusting the model parameters. Additional constraints on magnetic fields arise from the considerations of baryogenesis and, possibly, from the Schwinger effect of creation of charged particle-antiparticle pairs.*Y.V. Shtanov* - The possible dark matter signal has been searched in the X-ray astrophysical observation data. The surface brightness distribution of the 3.5 keV dark matter candidate line was obtained within the Galactic halo. This distribution was used to update the previous estimates of the sensitivity of the forthcoming dedicated mission Micro-X. The prediction for the width of the dark matter decay line in the future XRISM observations of the Perseus cluster was obtained with the use of cosmological hydrodynamical simulations.
*D.A. Iakubovskyi* - From the combined analysis of the kinematic data of the dwarf spheroidal galaxies, a new lower bound of ~200 eV on the dark matter fermion mass was obtained. It was shown that it is impossible to constrain robustly the mass of dark matter particle from the cosmological absorption signal on frequencies 75-80 MHz (“21-cm absorption feature”). The detection of this signal was suggested by EDGES collaboration.
*A.V. Rudakovskyi, D.O. Savchenko, D.A. Iakubovskyi*

Department for High-Density Energy Physics

- A modification of the collinear evolution equations as an appropriate approach to improving the behavior of parton distribution functions in the region of small longitudinal momentum fractions and to finding more theoretical arguments to clarify the possible appearance of saturation regime is suggested.
*Corr. Member of NAS of Ukraine G.M. Zinovjev* - Basing on the theorems of analytic S-matrix theory and the dispersion relations for the elastic scattering amplitudes it is shown that contribution of the odderon, crossing-odd component of the amplitude, dominates at high energies in the ratio of real to imaginary part of the amplitude. Asymptotically, these ratios have opposite signs for proton-proton and proton-antiproton scatterings.
*E.S. Martynov, G.S. Tersimonov* - A single component quantum Van der Waals equation of state of hard spheres from quantum partition function was derived for the first time. The suggested analytical method of self-consistent calculation of the excluded particle volume in a dense medium is generalized for the hard sphere mixture of arbitrary number of different hard-core radii. The quantum equation of state is extrapolated to high densities and generalized for the mixtures of convex hard particles of arbitrary shape for spatial dimensions D ≥ 2
*K.A. Bugaev* - Backward nucleon production by heavy baryonic resonances in proton-nucleus collisions is proposed.
*M.I. Gorenstein* - On the basis of the integrated hydrokinetic model the full similarity of “soft physics” processes in nuclei collisions of gold at the energies per nucleon pair of 200 GeV at RHIC, lead at the LHC energies 2.76 and 5.02 TeV, and xenon at 5.44 TeV has been found.
*Yu.M. Sinyukov, V.M. Shapoval, M.D. Adzhymambetov* - The thermodynamically consistent mean-field model is applied to describe dense boson systems for high temperatures and zero chemical potential. It is shown that if the attractive component is strong enough to violate the system-stability condition (the effective particle mass is greater than or equal to zero), then the first-order phase transition occurs in the multi-boson system and scalar field condensate is formed. The allowed states of the system with the condensate are shown to exist under the condition that the effective mass particle vanishes, i.e., the boson quasi-particles become massless.
*D.V. Anchishkin*

Department for Theory of Quantum Processes in Nanosystems

- The physics of long-range electron transfer in nanoscale molecular structures associated with molecular wires was clarified along with analytical description of a tunneling current through terminated molecular wires. These expressions allowed us to explain the dependence of the current-voltage characteristics of a molecular wire on the length of its interior range as well as the parameters of superexchange model used.
*Corr. Member of the NAS of Ukraine E.G. Petrov* - Analytical formulas are obtained that are convenient for describing the experimental results of the tunneling conductance of molecular chains. The wide abilities of the modified super-exchange model in understanding the mechanisms of conductivity formation were demonstrated, which was manifested in the analysis of coherent electron tunneling through alkane chains attached to electrodes by various anchor groups.
*Corr. Member of the NAS of Ukraine E.G. Petrov, Ye. V. Shevchenko* - The theory on the magnetic field energy absorption by metal nanoparticles of a nonspherical shape irradiated with ultrashort laser pulses is developed. The dependence of this energy on the orientation of the magnetic field upon a particle, the degree of its deviation from a spherical shape, and pulse duration of the laser ray has been scrutinized for the particles having an oblate or prolate spheroidal shape.
*N. I. Grigorchuk* - The electron transfer from the barrier in binary InAs/GaAs quantum dot-well structures was described in terms of localized and delocalized states and their spectral distributions. It was shown that theoretical calculations agree well with the optical experiments for these nanostructures.
*S.P. Kruchinin* - Exact solution to the problem of a closed description of the nonautonomous dynamics of a two-stage absorbing Markov chain with the presence of a stochastic dichotomous process in the forward or backward probabilities of transitions between initial and intermediate states is provided. It is shown that the kinetics of decay of the intermediate-state population is four-exponential that gives evidence for an intrinsic non-autonomy of a two-stage absorbing Markov chain with stochastic forward rate.
*V.I. Teslenko, O.L. Kapitanchuk*

Department for Mathematical Methods in Theoretical Physics

- Model of dark matter, which was constructed on the basis of μ-deformed thermodynamics, has been developed to describe halo density profiles from the dark matter around dwarf galaxy. Herein, μ-deformed analogs of the Lane-Emden equation were constructed, and their solutions have been found. As result, the use of μ-deformation leads to improved agreement with observational data as compared to the well-known models (T. Harko and Navarro-Frenk-White ones). Possible physical meaning of the parameter μ is briefly discussed.
*A.M. Gavrilik, I.I. Kachurik, M.V. Khelashvili* - For the model of the slowly rotating Bose-Einstein condensed dark matter, under the equilibrium condition the partition function and macroscopic characteristics are computed and compared with the results following from the Gross-Pitaevskii equation solution. Using the found Green functions of operators of spatial evolution, the boundary conditions of the problem and the conditions of applicability of the Thomas-Fermi approximation are formulated in a unified way. The deformation of the commutation relations for the macroscopic wave function and the corresponding modification of the Gross-Pitaevskii equation yields a spatial distribution of dark matter, similar to the model with rotation, which describes well the observed data. Such an assumption about the properties of dark matter leads to the spatial inhomogeneity of entropy and the dependence of the distribution on temperature (below the Bose-condensation temperature).
*A.V. Nazarenko* - We consider the grand canonical ensemble of the static and extremal black holes, when the equivalence of the electric charge and mass of individual black hole is postulated. Assuming uniform distribution of black holes in space, we are finding the effective mass of test particle and mean time dilation at the admissible points of space, taking into account the gravitational action of surrounding black holes. Having specified the statistics that governs extremal black holes, we study its effect on those quantities. Here, the role of statistics is to assign a statistical weight to the configurations of certain fixed number of black holes. We borrow these weights from the Bose-Einstein, Fermi-Dirac, classical and infinite statis-tics. Using mean field approximation, the aforementioned characteristics are calculated and visualized, what permits us to draw the conclusions on visible effect of each statistics.
*A.M. Gavrilik, A.V. Nazarenko* - In view of the problem of separation of variables for integrable hamiltonian systems with
*gl(n)*-valued Lax matrices, satisfying quadratic Poisson brackets with skew-symmetric classical*r*-matrices, we have found, in terms of the corresponding*r*-matrices, the sufficient conditions which guarantee that the “magic recipe of Sklyanin“ indeed produces canonical coordinates. An example of*gl(n)*⊗*gl(n)*valued skew-symmetric trigonometric*r*-matrix, that satisfies the obtained conditions, is considered and a class of the Lax operators is found, for which the obtained set of canonical coordinates is complete.*T.V. Skrypnyk* - An approach to define single-point interactions under the application of external fields has been developed. The essential feature is an asymptotic method based on the one-point approximation of multi-layered heterostructures that are subject to bias potentials. In the zero-thickness limit, the matrix connecting the two-sided boundary conditions of wave function at the point of singularity has been obtained. The dependence of the reflection and transmission coefficients on the bias potential has been studied. Several “one-point” models of two- and three-terminal devices in the semiconductor physics have been elaborated. The notion of a “point” transistor has been introduced, and the existence of extremely sharp peaks as an applied voltage tunes, forming a resonance set for this one-point interaction, is shown.
*A.V. Zolotaryuk, Y. Zolotaryuk*

Department for Theory of Nonlinear Processes in Condensed Matter

- Based on the Dirac quantum theory of the spinor field, the generelized operator of the spin-orbit interaction is found. It is shown that this operator contains not only the known Thomas-Frenkel correction, but also a new term, so that the consistent description of the influence of the spin-orbit interaction on electrons in the external potential in frame of the non-relativistic Schroedinger equation is possible only with the account of this generelized operator.
*L.S. Brizhik. O.O. Eremko, Acad. of the NAS of Ukraine V.M. Loktev* - An explanation is proposed for the recently observed a giant increase of the Drude peak width under applied uniaxial strain in optical spectra of monolayer graphene. The underlying mechanism of this increase can be based on resonant scattering of carriers from inevitably present impurities such as adsorbed atoms that can be described by the Fano-Anderson model. It is demonstrated that the often neglected scalar deformation potential plays the essential role in this process. The conditions necessary for the maximum effect of the giant Drude peak broadening are determined.
*V.O. Shubnyi, Y.V. Skrypnyk, S.G. Sharapov, Acad. of the NAS of Ukraine V.M. Loktev* - Two types of general nonlinear integrable systems on infinite quasi-one-dimensional regular lattices are proposed. The method is suggested which allows to unify the Toda-like vibration subsystem and the self-trapping-like exciton subsystem into a single integrable system, thereby substantially extending the range of realistic physical problems that can be rigorously modeled. Several lowest conserved densities associated with either of the relevant infinite hierarchies of local conservation laws are found explicitly in terms of prototype field functions.
*O.O. Vakhnenko* - The properties of embedded solitons (solitons that exist despite their resonance with the linear spectrum of the system and have only isolated values of velocity) in the discrete double sine-Gordon equation with next-neighbor and second-neighbor interactions are investigated. This model describes the DC biased array of the superconductor/ferromagnet/ superconductor junctions. Depending on the sign of these interactions they can be either destructive or favorable for the embedded soliton creation. The embedded soliton existence area depends on the width of the linear spectrum: narrowing of the spectrum widens the embedded soliton existence range and vice versa.
*Ya. Zolotaryuk, I. Starodub* - An approach to define single-point interactions under the application of external fields has been developed. The essential feature is an asymptotic method based on the one-point approximation of multi-layered heterostructures that are subject to bias potentials. In the zero-thickness limit, the matrix connecting the two-sided boundary conditions of wave function at the point of singularity has been obtained. The dependence of the reflection and transmission coefficients on the bias potential has been studied. Several “one-point” models of two- and three-terminal devices in the semiconductor physics have been elaborated. The notion of a “point” transistor has been introduced, and the existence of extremely sharp peaks as an applied voltage tunes, forming a resonance set for this one-point interaction, is shown.
*A.V. Zolotaryuk, Y. Zolotaryuk* - The interaction of hydrogen peroxide and water molecules with the regions of specific and non-specific recognition of DNA molecules by proteins is analyzed. These interactions are important for explanation of beam therapy of cancer. On the basis of density functional theory, the interaction energies of water and hydrogen peroxide molecules with DNA nuclear bases are calculated and optimal geometries of stable complexes are determined. The positions are found where binding of hydrogen peroxide molecule exceeds the one for water molecule.
*S.N. Volkov, D.V. Piatnytskyi, O.O. Zdorevskyi* - The interaction of polyamines with the DNA macromolecule was studied using molecular dynamics simulations. The polyamines molecules were found to be localized mostly in the minor groove of the double helix in the region with the specific sequence of nucleotides of A-tract type. The results of the study agree with the existing experimental data and explain the preferential localization of polyamines molecules in the DNA sites with characteristic nucleotide sequence.
*S.M. Perepelytsya*

Department for Synergetics

- It is proposed the new approach to the description of liquid crystal under the assumption that colloidal particle can be treated as a source of possible deformation of the ground state of the director field distribution.The ground state imposes restrictions on possible deformations and determines the peculiarity of the interaction between colloidal particles. On the basis of this approach, both the Coulomb-like interaction between dipole particles in a cholesteric liquid crystal and a crucial change in the character of the interaction in a smectic liquid crystal had been predicted.
*Corr. Member of the NAS of Ukraine B.I. Lev* - The exact solution of the classical and quantum cosmological model with exponential dependence on fundamental scalar field potential in homogeneous and in-homogeneous cases has been obtained. A new solution of the Universe evolution model was found at the inhomogeneous change of scalar field.
*Corr. Member of the NAS of Ukraine B.I. Lev, A.P. Rebesh* - The simple model for explanation experimental result about rotation of elongate particle at external electric field has been proposed. The model based on collective behavior of assembly of the particles with induced dipole moment.
*Corr. Member of the NAS of Ukraine B.I. Lev* - The theory of collective diffusion effects in a system of colloidal particles in a liquid crystal is proposed. The specifics of diffusion which can be observed experimentally are described. The dependence of the diffusion coefficient on the temperature and particle density is found. It is shown that collective diffusion in a system of colloidal particles in a liquid crystal arises from the elastic distortion of the director field generating the interparticle interaction.
*Acad. of the NAS of Ukraine A.G. Zagorodny, Corr. Member of the NAS of Ukraine B.I. Lev* - On the basis of non-equilibrium statistical operator with a view to describe a behavior of self-gravitating systems it has been proposed the new approach, which takes into account a possible spatially nonuniform distribution of particles, chemical potential, and temperature. Statistical induced dynamic and behavioral peculiarities of self-gravitating systems under different conditions have been theoretically predicted.
*Corr. Member of the NAS of Ukraine B.I. Lev* - Explicit expressions are found for the stationary probability distribution of a magnetic field, generated by moving charges of the plasma environment, and stationary probability distribution of force, acting on a charged particle in this environment with regard for its interaction with electric and magnetic fields in plasma.
*Acad. of the NAS of Ukraine A.G. Zagorodny, Corr. Member of the NAS of Ukraine B.I. Lev, V.B. Tymchyshyn* - The kinetic theory of electric fluctuations in a collisional weakly ionized dusty plasma is formulated with due regard to the grain charging dynamics. The correlation functions of electron and ion density are obtained by considering their collisions with neutrals described within the Bhatnagar-Gross-Krook model. The electron density correlation spectra in isothermal and nonisothermal plasma are calculated for various values of grain density, grain size, and ion collisionality.
*Acad. of the NAS of Ukraine A.G. Zagorodny* - The theory of tokamak transport due to drift waves is revised. The development of the theory has been analized, starting with simple theories from the 1950s till today advanced theories using improved fluid models taking full account of kinetic effects in the frequency regime of drift waves, also including the effects of zonal flows, and fully nonlinear kinetic theory itself. An exact fluid closure makes it possible to use fluid theory completely without expansion, thus maintaining the fluid resonances due to magnetic drifts, that gives us a new normalization of drift wave equations and enables to recover nonlinear (Dimits) upshifts, spinup of poloidal rotation in internal transport barriers and the L-H transition.
*Acad. of the NAS of Ukraine A.G. Zagorodny* - On the basis of the developed analytical method, as well as by numerical simulation, the dependences of the transport coefficient of charged particles across a magnetic field on a frequency of a random electric field were found. It is shown that the results of the calculations are consistent with the data of direct numerical simulation over a wide frequency range. The results obtained can be useful for optimizing the performance of plasma devices in which processes of anomalous diffusion are significant.
*V.I. Zasenko, O.M. Cherniak* - A new mechanism for the selectivity enhancement of secondary neurons of the olfactory system is proposed, which operates at low odor concentrations when previously known mechanisms are ineffective.
*A.K. Vidybida* - For a class of neuronal models the spiking statistics of inhibitory neuron with delayed feedback stimulated with stochastic renewal point process is described. The explicit formulas without applying diffusion approximation have been found.
*A.K. Vidybida, O.V. Shchur* - A mathematical model of the open dissipative system with localized metabolic process involving anaerobic bacteria is presented. The general map of its metabolic paths is constructed. The synergetic method to study the self-organization of a dynamical chaos in metabolic processes in a cell and the whole organism is developed.
*V. Grytsay* - A model is worked out of the biochemical process of cellulose hydrolysis associated with the growth of cells and biosynthesis of enzymes. The model proposed describes an active medium that is an open system with the input and dissipation of both substance and energy in terms of a dynamical system of 6 nonlinear differential equations. The results obtained contribute to the general theory of nonequilibrium systems and refine the universality of the self-organization laws in nature.
*A.S. Zhokhin* - Strategies optimizing continuous-variable teleportation of a quantum-light mode through the turbulent atmosphere have been proposed.
*A.A. Semenov* - The principle of equilibrium of the open economy with its environment is formulated: the national currency exchange rate relative to the USA dollar is an indicator of the equilibrium the economy to its environment. Using this principle the canonical money circulation equation in the economy is established. On the basis of this equation the principle of the sustainable economy development is formulated. Outside of such a state the economy can be in the state of recession or in the state being close to it. On this basis the classification of the equilibrium states of the economy are given.
*M.S. Gonchar, O.P. Dovzhyk*

Department for Theory of Nuclei and Quantum Field Theory

- The theory of polarization of the vacuum of quantized fermion field in the presence of a topological defect is constructed.
*Corr. Member of the NAS of Ukraine Yu.A. Sitenko* - Using the method of stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere, the analytical solution of the two-particle Lippmann-Schwinger integral equation with the Coulomb interaction at the negative energy has been performed. For the first time, the analytical expressions for the three-dimensional Coulomb transition matrix at the energies that correspond to the fractional values of the interaction parameter have been obtained.
*V.F. Kharchenko* - The simple semi-phenomenological model which describes the charge independence and charge symmetry breaking of the pion-nucleon coupling constant has been proposed. The model has simple physical meaning and suggests directly proportional dependence of the pion-nucleon coupling constants on the masses of interacting nucleons and pions. On the basis of the proposed model we have found that the charged pion-nucleon coupling constant exceeds the neutral pion-nucleon coupling constant by about 7% indicative of a substantial charge independence breaking of nuclear forces in the pion-nucleon coupling constant.
*V.A. Babenko, N.M. Petrov*

Department for Computer Maintenance

- Thanks to the financial support of the NAS of Ukraine in 2019, modern server equipment was purchased and a cloud cluster was installed at the Collective Use Center “Resource Center for Grid and Cloud Technologies” at the Bogolyubov Institute of Theoretical Physics of the NAS of Ukraine. 10 computing servers based on Intel (R) Xeon (R) Silver 4116 CPUs and Intel (R) Xeon (R) Silver4216 CPUs form the basis of the cloud cluster. Currently, the total cloud cluster processing power is 576 virtual processors, 2560 Gb of RAM and 200 Tb of storage. For all servers the Ubuntu Server 18.04.2 LTS x64 operating system has been installed and OpenStackRocky cloud-based services have been deployed. Subsequently, the certification of the cloud cluster in accordance with the requirements of the EGI FederalCloud project was carried out and, after successful testing, the cloud cluster (registration name – UA-BITP) was put into technological operation. At present, the UA-BITP cloud site is the only one cloud resource in Ukraine that meets all of EGI FederalCloud's cloud resource requirements and includes the European cloud infrastructure to support the European Open Science Cloud. Due to the high reliability of work and the provision of computational resources for sharing, the international scientific cooperation of researchers of NAS of Ukraine in such fields as high energy physics and astrophysics, molecular biology, cell biology, Earth sciences and other ones is increased.
*S.Ya. Svistunov, I.M. Makovsky, V.V. Pelykh*