Department for Astrophysics and Elementary Particles

- We argue that the correct definition of the electric current in the chiral kinetic theory for Weyl materials should include the Chern-Simons contribution that makes the theory consistent with the local conservation of the electric charge in electromagnetic and strain-induced pseudoelectromagnetic fields. By making use of such a kinetic theory, we study the plasma frequencies of collective modes inWeyl materials in constant magnetic and pseudomagnetic fields, taking into account the effects of dynamical electromagnetism. We show that the collective modes are chiral plasmons. While the plasma frequency of the longitudinal collective mode coincides with the Langmuir one, this mode is unusual because it is characterized not only by oscillations of the electric current density, but also by oscillations of the chiral current density. The latter are triggered by a dynamical version of the chiral electric separation effect. We also find that the plasma frequencies of the transverse modes split up in a magnetic field. This finding suggests an efficient means of extracting the chiral shift parameter from the measurement of the plasma frequencies in Weyl materials.
*E.V. Gorbar* - It is shown that the non-exponential form of the diffraction cone observed in the elastic scattering of protons by the LHC accelerator is a confirmation of the presence of a pion “coat” in protons associated with the analytic properties of the scattering amplitude.
*L. Jenkovszky* - Using the dark matter density profiles from literature we have selected the 19 galaxy clusters with the largest expected dark matter decay flux. We processed all XMM-Newton public observation data for this objects. The emission spectra were modeled as sum of continuous plasma emission and known astrophysical lines. The fluxes of faint lines (e.g. K at 3.51 keV) were limited from above using fluxes of significantly detected lines. In 6 of spectra we identified >2σ positive residuals with average position

3.56±0.02 keV in the emitters frame. Their observed properties are unlikely to be explained by statistical fluctuations or astrophysical emission lines. Our detailed simulations showed that the combined significance of these detections equals to at least 2.6σ, raising to 3.2σ taking the line energy variation into account. Fitting the line position in observers frame prefers the astrophysical origin of line signal over instrumental one, with atomic line emission being included in the fitting models. Interpreting the new line due to decaying dark matter gives the radiative decay lifetime τDM≈(3.2−5.3)×10^{27 }s consistent with previous detections.*D.A. Iakubovskyi, D.O. Savchenko*

Department for High-Density Energy Physics

- Significantly alternative mechanism for thermal radiation of photons and di-leptons is suggested. It is based on an effect of synchrotron radiation that arises from the interaction of quarks with collective color field providing a confinement. The intensity of such a radiation for the hot medium of size 1-10 fermi (that just is expected in the collisions of relativistic heavy ions) tuгns out quantitatively very close to standard volume photon radiation at temperatures
*T*=200-300 MeV. The most striking feature of such a mechanism is the high degree of polarization of photons. It has been found out the virtual photons develop the noticeable specific anisotropy in the angle distribution of leptons with respect to the three-momentum of pair and is shown such a radiation is will be non-isotropic for the non-central collisions. Such an angular anisotropy is absent in the Drell-Yan mechanism and the other “standard volumetric” mechanisms and could be (if discovered experimentally) quite reliable signal of creating quark-gluon plasma in the relativistic collisions of hadrons and heavy ions.*Corr. Member of the NAS of Ukraine G.M. Zinovjev* - The newest data of the TOTEM Collaboration at 13 TeV and all the present data on the total cross sections together with ratios of real to imaginary part of elastic forward scattering amplitudes at energies higher than 5 GeV have been analyzed. As a result the serious arguments have been presented, and the surprisingly small value of this ratio 0.098±0.01 measured in TOTEM experiment сlearly showed the first experimental observation of an “odderon” in its maximal form.
*Ye.S. Martynov* - The model of hadron resonance gas that includes an effect of interaction between baryons has been developed and used to calculate the baryon number fluctuations, in particular, the cumulants of third and fourth order in order to describe the results of the central nuclei-nuclei collisions.
*M.I. Gorenstein* - Using the proposed equation of state with the induced surface tension which allows one to go beyond the Van der Waals approximation the thermodynamic properties of hadronic matter at chemical freez-out are fixed with high confidence for the temperature
*Т*=50-170 МеV and baryonic chemical potential*μ*= 0-770 MeV. Fitting the experimental data on hadronic multiplicities the equation of phase state that is created at the center of mass collision energies of nuclei in the interval √s = 4.9-9.2 GeV/nucl has been found for the first time, and the strong arguments in favor of this phase as a phase of nearly massless hadrons have been given. Thus, it leads to the conclusion about existence of a tri-critical endpoint, but not a critical one, in the QCD matter.*K.A. Bugaev, V.V. Sagun, A.I. Ivanytskyi, Corr. Member of the NAS of Ukraine G.M. Zinovjev* - The meson resonance K * (892) with the lifetime of 4-5 fm/s are used as a probe to analyze a spaсe-temporal picture of nuclear-nuclear collision processes. It is found that almost half of these mesons are born inside a hadron environment and 70% of their decay products interact with the medium. It testifies to the existence of dense hadron matter with a life time not less than 5 fm/c after the quark-gluon plasma hadronization. The numerical calculations of this picture within the integrated hydrokinetic model lead to the results fitting well the LHC experimental data.
*Yu.M. Sinyukov, V.M. Shapoval*

Department for Theory of Quantum Processes in Nanosystems

- The kinetics of electroluminescence formation is studied in the nanosystem “metal-molecule-metal” with symmetric and asymmetric couplings of the molecule to the contacts. It is shown that the optically active state of the molecule is formed as a result of hopping electrons between the molecule and each of the electrodes, as well as due to inelastic interelectrode tunneling of the electron. The conditions for the enhancement of electroluminescence power caused by interface structure and transformation of molecular spectrum, are found for chromophoric molecules.
*E.G. Petrov, V.O. Leonov, Ye.V. Shevchenko* - Peculiarities of electron energy relaxation on lattice vibrations in metal are investigated. The analytical formula for electron energy looses per time (necessary for excitation of acoustical lattice vibrations) is obtained. It is shown that the amount of power absorbed by lattice is determined by the relations between Debye temperature and lattice temperature as well as between lattice temperature and electron temperature.
*N.I. Grygorchuk* - Time-dependent density functional theory calculations were applied to explain photoinduced ring-closing mechanisms of a difurylethene molecule studied by femtosecond transient absorption spectroscopy. Calculated excitation spectra, potential energy surfaces and switching barrier of cyclization reaction predict possible relaxation paths of the molecules when open form is excited by different wavelengths of the pump pulse.
*O.L. Kapitanchuk* - With the advent of high-precision single-molecule spectroscopy and the possibility to monitor reactions of single enzymes as well as to control their function, the necessity of revising the classical enzymatic catalysis schemes and deviations from the latter has come to the fore. Using the developed stochastic approach, we perform a theoretical analysis of kinetics of the main Michaelis-type schemes with allowance for dynamic disorder in either the free enzyme or enzyme-substrate complex in the cases of discrete set of conformations or bounded structural diffusion. New, sometimes counter-intuitive dependences of the enzymatic reaction velocity on substrate concentration and parameters of the reaction scheme are revealed.
*L.N. Christophorov*

Department for Mathematical Methods in Theoretical Physics

- Bose-condensate models of dark matter are rather popular, however possess some difficulties. We consider the
*μ*-Bose gas model which is a deformation of Bose gas model (BGM) with rational type of nonlinearity, and at*μ*=0 reduces to the BGM. Within thermodynamic geometry of*μ*-BGM, the scalar curvature is calculated and its singular behavior is found. It confirms a presence of condensate in the system of*μ*-bosons. Using this fact and other important properties of*μ*-BGM which give some advantages relative to BGM, the application of the*μ*-deformed system for effective modeling of dark matter surrounding dwarf galaxies is proposed.*A. Gavrilik, I. Kachurik, M. Khelashvili, A. Nazarenko* - For the one-dimensional Schrödinger equation, which describes the electron tunneling through a two- or three-layer heterostructure, in a single-point approximation, the effect of splitting resonant-tunneling levels into the countable sets, having the form of curves or surfaces that depend on two or three layers of the structure, has been observed and described in detail.
*A.V. Zolotaryuk* - An explicit solution of the rank
*N*Fuji-Suzuki-Tsuda system with*n*singular points in terms of semidegenerate*n*-point conformal blocks of W_{N}-algebra with central charge*c=N*-1 is constructed. This construction uses different properties of conformal blocks of W_{N}-algebras. Although these properties are well known, some of them were proved for*N*>3 for the first time: (1) for arbitrary central charge a reduction of three-point conformal blocks to a minimal set of conformal blocks is given; (2) for*c=N*-1 for the degenerate field on the second level the restrictions on the fields to have non-zero three-point conformal blocks were found; (3) formula for the four-point conformal blocks with one semi-degenerate and one degenerate fields in terms of generalized hypergeometric functions is proved.*P. Gavrylenko, N. Iorgov*

Department for Theory of Nonlinear Processes in Condensed Matter

- A new mechanism of point mutation formation in biological systems that takes into account the fluctuation appearance of complementary pairs preopened by water in the DNA double helix has been proposed. The possible proton transitions in the preopened A-T pair have been analyzed within the density functional theory, and their energies have been numerically obtained. It is shown that under formation of an opened pair, irregular tautomeric forms of the nucleic bases can be stabilized and be the origin of point mutations. The estimated probability of the occurrence of these mutations in DNA falling in the interval of 10
^{-10}-10^{-11}explains the known experimental facts.*E.S. Kryachko, S.N. Volkov* - The mixed set of primary and intermediate fields for the integrable nonlinear Schrödinger system on a triangular ladder lattice is found out. Having been written in terms of these field variables the system is shown to split into two subsystems with qualitatively different properties of excitations. The crossover effect in the system dynamical behavior at the critical value of background parameter is established.
*О.О. Vakhnenko*

Department for Synergetics

- We report the first direct observation of Coulomb-like elastic interactions between colloidal particles in a nematic liquid crystal predicted theoretically. The interaction of two particles located at the boundary of twist and parallel aligned regions is observed. We demonstrate that such particles produce deformation elastic charges responsible for Coulomb-like interactions.
*Corr. Member NASU B.I. Lev* - The mechanism of the colloidal particle motion is proposed for liquid crystals with deformed director field. It is shown that the translation motion of colloidal particles depends on the specific deformation of the elastic field.
*Corr. Member NASU B.I. Lev* - A new approach which employs a non-equilibrium statistical operator that takes into account inhomogeneous distribution of particles and temperature is proposed. The method involves a saddle-point procedure to find the dominant contributions to the partition function. The equation of state for self-gravitating systems has been determined.
*Corr. Member. NASU B.I. Lev* - A formalism to describe an equilibrium based on consideration of a macroscopic but finite volume has been proposed. The presence of a Bose-Einstein condensate is taken into account through an off-diagonal long-range order in the transition to the thermodynamic limit. On this basis, the degenerate Bose-gas with delta-shaped interaction potentials has been described in term of self-consistent Hartree-Fock approximation. The explicit expressions for the energy spectra of single particle and collective excitation have been obtained.
*Acad. NASU A.G. Zagorodny* - The exact solution is found for the model of nonlinear oscillator with the coordinate-dependent mass, or velocity-dependent elastic modules. The Poincare cross-sections are studied and the conditions of the stochastic behavior of the oscillator motion are found experimenatally.
*Acad. NASU A.G. Zagorodny, Corr. Member NASU B.I. Lev, V.B. Tymchyshyn* - For wide class of neuronal models it is proven mathematically rigorous that activity of fast CL-type inhibitory neuron with delayed feedback stimulated with a renewal stochastic stream is non-Markovian one.
*A.K. Vidybida* - A physical mechanism is proposed for information reduction in a neuronal network through merging of different trajectories into a single one with subsequent entrainment onto a periodic regime. It is established that neuronal firing is a necessary prerequisite for merging. For a wide class of neuronal models for spiking inhibitory neuron with fast CL-type inhibitory delayed feedback a possibility to present the output statistics through the statistics for of that same neuron without feedback and the delay line characteristics. Exact mathematical expressions for such a representation are derived.
*A.K. Vidybida, O.V. Shchur* - The metabolic process in a cell is modeled using the Fourier transformation. The histograms of the invariant measures of chaotic attractors are constructed. Necessary number of harmonics, which represent uniquely the most complicated mode of a strange attractor, has been found. The dependence of the attractor type on the distributions and the harmonics amplitudes in the Fourier spectrum has been studied. The harmonics forming the laminar and turbulent parts of the attractor trajectory are identified. The projection histograms of the invariant measures of the main types of the system strange attractors have been constructed, and their dependence on the phase portrait has been determined.
*V.I. Grytsay* - Free-space optical communication links are promising channels for establishing secure quantum communication. We study the transmission of nonclassical light through a turbulent atmospheric link under diverse weather conditions, including rain or haze. Based on previous results, we study theoretically the transmission of quadrature squeezing and Gaussian entanglement under these weather conditions.
*D.Yu. Vasilyev* - We proposed a method to calculate the type of a lattice formed by grains in dusty plasma and to estimate its potential energy. Basically, this task is complicated by the interparticle potential that appertains to “catastrophic potentials”. This kind of potentials needs special approaches to avoid divergences during potential energy calculations. We developed all the necessary modifications to appropriate methods. It has been shown that the obtained potential energy expression could be used to determine lattice parameters and these parameters comply to known experimental data.
*Acad. NASU A.G. Zagorodny, Corr. Member. NASU B.I. Lev, V.B. Tymchyshyn* - The diffusion of charged particles in a static random electric field across the magnetic field is considered. A new closure of the statistical equation describing particle diffusion in a frozen field is proposed, taking into account the effects of particle trapping and finite Larmor radius without the assumption of its smallness. A direct numerical simulation was performed and it was shown that the statistical characteristics found as solutions of the analytical model are in agreement with the simulation results in a wide range of Larmor radii.
*Acad. NASU A.G. Zagorodny, V.I. Zasenko, O.M. Cherniak* - It has been presented a general concept of bank work description, based on investment strategy both in risk and risk-free assets, dynamics of deposit attraction and incomes from operational activity, dynamics of liability payments,. Using these factors, a stochastic model of bank capital evolution is constructed. The problem of assessment of bankruptcy probability, depending on the choice of strategy investment, the deposit attraction on bank accounts, the restrictions for the bank liability payments is solved. A quantitative characteristic of management quality is introduced. Under the condition that the quantitative characteristic is satisfactory the conditions for the factors introduced above are found under that a bank can function infinitely long time with the sufficiently small bankruptcy probability.
*N.S. Gonchar, W.H. Kozyrski, A.S. Zhokhin, L.S. Terentieva*

Department for Theory of Nuclei and Quantum Field Theory

- We consider quantum ground state effects in Dirac materials with two-dimensional monolayer structures warped into nanocones by a disclination; the nonzero size of the disclination is taken into account, and a boundary condition at the edge of the disclination is chosen to ensure self-adjointness of the Dirac-Weyl Hamiltonian operator. In the case of carbon, silicium and germanium nanocones, we show that the quantum ground state effects are independent of the disclination size and find circumstances when they are independent of the boundary parameter.
*Yu.A. Sitenko* - On the basis of Schwinger representation for the Coulomb Green function the possibility of the analytical solution of the Lippmann-Schwinger equation for the three-dimensional Coulomb transition matrix at negative energies has been established in the case of the repulsive interaction and the integer values of Coulomb parameter as well as in the case of repulsive and attractive interactions and half-integer values of Coulomb parameter (1/2 and -1/2, respectively).
*V.F. Kharchenko* - We considered a set of three-cluster systems (
^{4}He,^{7}Li,^{7}Be,^{8}Be,^{10}Be) within a microscopic model which involves the hyperspherical harmonics to represent intercluster motion. We selected such three-cluster systems which have at least one binary channel. Our aim is to study whether the hyperspherical harmonics are able and under what conditions to describe two-body channel or they are suitable for describing three-cluster continuum only. The main result of the present investigations is that to describe the nondemocratic two-cluster decay or bound states below the two-cluster threshold one needs to use a rather restricted set of the hyperspherical harmonics and hyperradial excitations as well. It was demonstrated that the eigenstates of the three-cluster hamiltonian have correct asymptotic behaviour both for bound states below two-cluster threshold and states in two-cluster continuum.*Yu.A. Lashko, G.F. Filippov, V.S. Vasilevsky* - On the basis of a simple phenomenological model, by assumption of the one-pion exchange mechanism for the nuclear forces, we establish relations between different pion-nucleon coupling constants that characterize the nucleon-nucleon interaction. The charge independence breaking effect in the pion-nucleon coupling constants is entirely explained by the mass difference between the charged and neutral pions and by the mass difference between the proton and the neutron as well.
*V.A. Babenko, N.M. Petrov*

Department for Computer Maintenance

- The support of the BITP industrial cloud infrastructure which is based on OpenStack and distributed filesystem Ceph was provided. The services to ensure reliable operation of the BITP industrial cloud infrastructure for guaranteed data processing of the ALICE experiment at CERN using the HTCondor system was developed and implemented to support the scientific computing.
*S.Ya. Svistunov*