Department for Astrophysics and Elementary Particles

- The gap equation for Dirac quasiparticles in monolayer graphene in constant magnetic and pseudomagnetic fields, where the latter is due to strain, has been studied in a low-energy effective model with contact interactions. By analyzing solutions of the gap equation, the phase diagram of the system in the plane of pseudomagnetic and parallel magnetic fields has been obtained. The three quantum Hall states, ferromagnetic, antiferromagnetic, and canted antiferromagnetic, are realized in different regions of the phase diagram. It is found that the structure of the phase diagram is sensitive to signs and values of certain four-fermion interaction couplings which break the approximate spin-valley SU(4) symmetry of the model.
*E.V. Gorbar, V.P. Gusynin* - Last year we have detected an X-ray emission line at energy around 3.5 keV in the spectrum of Andromeda galaxy and in the spectra of nearby galaxy clusters. Interpretation of this line as a signal from dark-matter decay places lower and upper bounds on its possible intensity from the region of Galactic Center. This year we have detected such an emission line at energy 3.539 ± 0.011 keV in the deep-exposure observation of the Galactic Center by the XMM-Newton X-ray observatory. The result obtained is consistent with the above constraints for a class of Milky Way mass models, and corresponds to radiative decay of dark matter with lifetime (6−8)×1027 sec. Although it is hard to exclude an astrophysical origin of this line based on the observations of Galactic Center alone, this result is an important consistency check of the dark-matter decay hypothesis that encourages to check it with future observational data.
*D.A. Iakubovskyi*

Department for High-Density Energy Physics

- Description of quantum liquids (Landau-Fermi liquids) resulting from the quark models with a four-fermion interaction has been given. This consideration is based on using a dressing Bogolyubov transformation and mean field approximation. It is demonstrated that the mean energy of the ensemble serves as energy functional of the Landau theory and is shown that in a wide range of potentials interesting for applications one can expect the quantum liquids to behave in essentially the same way. For some of their properties a band of estimates has been obtained. A comparison of Nambu-Jona-Lasinio and Keldysh models, substantially different in many aspects, demonstrates that the properties of quantum liquids do not actually depend on the shape of the form factor (a natural interaction length); rather, they are mainly determined by the coupling constant of the interaction. It is found out that a common distinctive feature of ensembles is the presence of degenerate states with respect to the vacuum in the chemical potential and pressure.
*G.M. Zinovjev* - The van der Waals (VDW) equation of state predicts the existence of a first-order liquid-gas phase transition and contains a critical point. The VDW equation with Fermi statistics is applied to a description of the nuclear matter. The nucleon number fluctuations near the critical point of nuclear matter are studied. The scaled variance, skewness, and kurtosis diverge at the critical point. It is found that the crossover region of the phase diagram is characterized by the large values of the scaled variance, almost zero skewness, and by the significantly negative kurtosis. The rich structures of the skewness and kurtosis are observed in the phase diagram in the wide region around the critical point, namely, they both may attain large positive or negative values.
*D.V. Anchishkin, M.I. Gorenstein* - From the analysis of more experimental hadronic multiplicities, than there were used before, we found at chemical freeze-out two peaks of the dimensionless measure of interaction at the center of mass collision-energies 4,9 GеV/nucl and 9,2 GеV/nucl. The strong model arguments that these two peaks provide evidence of two phase transformations at these collision energies are given. The higher peak at the collision energy 4,9 GеV/nucl gives evidence of the first order phase transition, while the smaller peak at higher energy of collision is related either to a second order phase transition or a weak cross-over.
*K.A. Bugaev, V.V. Sagun, A.I. Ivanytskyi, G.M. Zinovjev* - The integrated hydrokinetic model of nucleus-nucleus collisions has been developed and successfully applied for description and predictions of the experimental data. The model includes the generation of the initial state of matter formed in these collisions, its thermalization and subsequent viscous hydrodynamic evolution, decay into separated hadrons, and the final stage – the evolution of non-equilibrium gas of interacting hadrons and resonances.
*V.Yu. Naboka, Yu.M. Sinyukov*

Department for Quantum Theory of Molecules and Crystals

- A microscopic model of quantum transitions in the generalized few-level system has been proposed. Several mechanisms of variation of the positions of energy levels have been taken into account for a coarse-grained description of flexible macromolecular structures with the hierarchy of characteristic times. Particularly, the additions from an initial chaotization of energy levels, their adiabatic stochastization, as well as their nonadiabatic relaxation have been determined. For the general case of chaotic distribution of fluctuating energy levels, weakly coupled with the environment, the probabilities of between-level transitions have been found in the analytical form. This expression comprises an explicit dependence on dimensionality of the energy levels, their stochastic broadening and their relaxation coupling parameters for environment-induced transitions, thus leading to formation of the physical conditions for effective functioning of biomacromolecules
*E.G. Petrov, V.I. Teslenko, O.L. Kapitanchuk, V.O. Leonov* - A formation of stationary current and electroluminescence in a molecular diode in the case of asymmetric coupling of the molecule to the attached electrodes has been studied in the framework of kinetic theory of electron transport. The conditions have been found when a photocurrent as well as an electroluminescence achieves their maximum values. These conditions are realized when energy of the photoexcited molecule in the diode becomes, under the interelectrode bias voltage as well as the electric field of the gate electrode, lower the energy of the single-charged molecule. It is shown that both mechanisms of interelectrode electron transport associated with the sequential electron hoppings and the inelastic tunneling, contribute to the excitation of the molecule during a resonance regime.
*E.G. Petrov, Ye.V. Shevchenko, V.O. Leonov* - A kinetic model is developed to describe the of a few-phase ligand-receptor structure in the condensed medium. The rate constant for transitions between the energy levels of system has been found with regard for the dynamic, fluctuation and entropic system's parameters, and a ligand concentration and environment temperature as well. In the case of irreversible dynamics of level populations, the concentration dependences of their peak amplitudes are shown to acquire anomalous character. In particular, the log odds of the output state with respect to the cooperativity of the transient process is fractional and is limited from below by the quantity 2/е. Moreover, the approach of the log odds to this value is critical and leads to the break in the stability of the irreversible system. For low temperature, this effect occurs within a rather narrow range of rates of kinetic stages. The temperature increase diminishes the effect and thus increases the degree of control of the transient process
*V.I. Teslenko, O.L. Kapitanchuk* - Laser-pulse induced transient currents through a molecular junction are studied in the framework of a density matrix theory. By focusing on the sequential transport regime the effects of collective plasmon excitations of the leads are investigated. A remarkable current enhancement of transient as well as time-averaged dc currents is found due to simultaneous plasmon excitations in the leads. The effects of intra-molecular vibrational energy redistribution and its important role on both transient and the averaged dc-currents are also considered. A vibrational progression becomes visible if the dc caused by a huge sequence of laser pulses is drawn versus the applied voltage. This can be considered as a dynamically determined IV-characteristic.
*Y. Zelinskyy* - The orderings of classical one-dimensional structures of charges have been investigated in equilibrium states of Coulomb clusters with a confining potential originated from the uniform cylindrical background. Regions of parameters compatible with ideal structures or quite ideal ones on a finite length scale have been defined. Specificity of the physical mechanism that results in the high ordering of structures is discussed. Characteristics of ideal structures have been obtained and the algorithm for estimations of orderings in one-dimensional structures in a general case has been given.
*S.Ya. Goroshchenko* - A theory of triplet excitation transfer in a donor-oxygen-acceptor systems is developed for the conditions when the transfer is mediated by an oxygen molecule. It is shown that the oxygen molecule can be involved in both real and virtual intramolecular singlet-triplet conversions in the course of the process under consideration. Expressions describing a superexchange donor-acceptor coupling owing to a participation of the bridging twofold degenerate oxygen's virtual singlet state are derived and the transfer kinetics including the sequential (hopping) and coherent (distant) routes are analyzed. Applicability of the theoretical description to the pigment-protein cytochrome complex, by considering the triplet excitation transfer from the chlorophyll molecule to distant carotene, is explained using the above theoretical model.
*E.G. Petrov*

Department for Quantum Electronics

- The Hamiltonian and Poisson structures of integrable nonlinear Schrödinger system on a triangular-lattice ribbon have been found in the case of attractive nonlinearity.
*O.O. Vakhnenko* - A coupling between chiralities in spin and physical spaces has been found. The mechanism of the coupling is elucidated by using the Möbious ring as a case study. Due to the topology of the Möbious ring its ground state is a vortex state.
*V.P. Kravchuk, Yu.B. Gaididei* - The one-electron spectrum, eigenstates and Green functions of bounded graphene nanoribbons that describe electron dynamics have been found. On this basis, we obtained the analytic expressions for transmission coefficients for different carbon nanostructures. The obtained results have numerous applications to the construction of multi-terminal graphene-based electronic devices.
*L.I. Malysheva* - The mechanism of DNA deactivation under the irradiation of biological organisms by high energy ion beams has been introduced. Within the framework of this mechanism it is considered the formation of stable complexes of molecular products of water radiolysis (hydrogen peroxide) with the active centers of recognition of DNA double helix (РО
_{4}groups). The calculations of the complex energy show that DNA phosphate groups and counterions can form stable complexes with hydrogen peroxide molecules, which are as stable as the complexes with water molecules. The interaction of H_{2}O_{2}molecule with phosphate group of the double helix backbone can disrupt DNA biological function and induce the deactivation of the cell genetic apparatus.*D.V. Piatnytskyi, O.O. Zdorevskyi, S.M. Perepelytsya, S.N. Volkov* - The method of stabilization of the fluctuations of an optical free-space channel by means of beam expansion was proposed and experimentally studied. It was shown that if the fluctuations in the channel are concerned with the atmospheric effects which result in the beam wandering around the aperture, then the beam expansion allows one to stabilize the transmittance fluctuations at the same time reducing the mean transmittance. The realization of quantum communication through a stabilized channel was modelled theoretically and it was shown that for the given channel and other parameters there exists an optimal regime of fluctuation stabilization which enables the maximally effective communication.
*V. Usenko*

Department for Mathematical Methods in Theoretical Physics

- Recently it has been shown that the proposed by us two- and three-parameter deformed analogs of the Heisenberg algebra of position and momentum operators can be mapped onto respective algebras of non-standard deformed quantum oscillators. We have established that such relation dictates an unusual rule (instead of Hermitian) of mutual conjugation for the creation and annihilation operators a+and a-, namely the η(N)-pseudo-Hermitian conjugation, η(N) being certain operator function of the excitation number operator N. Respectively, that leads to η(N)-pseudo-Hermiticity of the position (or momentum) operator, whereas the Hamiltonian is Hermitian. Diverse possible cases have been described and specific properties related with η(N)-pseudo-Hermitian conjugation have been revealed.
*A.M. Gavrilik* - Integrable generalizations of the Jaynes-Cummings-Dicke models and the Bose-Hubbard-type dimers model, which are associated with general non-skew-symmetric classical r-matrices and Lie algebras of higher ranks, have been constructed. The spectrum of the Hamiltonians of integrable generalizations of Jaynes-Cummings-Dicke models and Bose-Hubbard-type dimers, associated with the twisted rational r-matrices and Lie algebras gl(n), have been found.
*T. Skrypnyk* - Within the problem of realization of composite (or quasi-) fermions, each of these consisting of a fermion and a deformed boson, the physical interpretation of the solutions and relevant parameters is analyzed in terms of deformed Fermi-oscillators. For the case of 2 modes of composite fermions and 2 or 3 modes of their constituents, i.e., ordinary bosons and fermions, the solutions are presented in the form symmetric under the interchange of quasi-fermion modes. General solution has been obtained in the case of non-deformed constituent boson and arbitrary number of modes of both composite fermions and their constituents. Particular solutions have been given, including those for maximally entangled states of composite fermions. The (inter-constituent) entanglement entropy has been obtained for composite quasi-fermions admitting the mentioned realization.
*A.M. Gavrilik, Yu.A. Mishchenko*

Department for Mathematical Modelling

- In exchange model, we found necessary and sufficient conditions for markets cleaning under given ownership and patterns of consumer demand structure. The theorem is proven describing the structure of ownership vectors in which for a given demand structure the complete cleaning of markets takes place. The equilibrium price vector is specified that provides such a cleaning. The theorem is proven, giving conditions of degeneracy multiplicity for equilibrium price vector. The concept of equivalent distribution of property is introduced, necessary and sufficient conditions are found for the existence of equilibrium price vector, and the structure of aggregate supply is described. A number of theorems is proven determining the aggregate vector of customer satisfaction levels. An adapted aggregated description of the economic system is proposed on the basis of input-output balance and is applied to the analysis of Great Britain, Germany, Russia and Greece economies.
*N.S. Gonchar, W.H. Kozyrski, A.S. Zhokhin*

Department for Theory of Nonlinear Processes in Condensed Matter

- Based on the solutions of the Dirac equation, it is shown that the system of quasi-two-dimensional electrons confined in the potential layer, for instance, in layered semiconducting heterostructures, can be in one of the three possible spin states. These states differ by spin polarization and by the spectrum of the two-dimensional energy zones. One of these states is a well-known Rashba state which is characterized by the spin splitting of energy zones. In the other spin state the spin splitting is anisotropic, and in the third state the energy zones are degenerate with respect to spin. Respectively, there are the three systems of eigenfunctions of the Dirac equation that correspond to the three spin states. The functions of each of these systems are also eigenfunctions of three different spin operators, which commute with the Hamiltonian of the Dirac equation, but do not commute with each other. These spin operators do determine the spin polarization of electrons.
*A. Eremko, L. Brizhik, V.M. Loktev* - We study the thermodynamic properties of the two-component 2+1-dimensional massive Dirac fermions in an external magnetic field. The violation of the time-reversal symmetry is shown to give rise to a term in the thermodynamic potential that is linear in the magnetic field, while the famous problem of Landau diamagnetism suggests that the leading field-dependent term is quadratic in the field. Accordingly, the leading term of the explicitly calculated magnetization is anomalous, viz. it is independent of the strength of the magnetic field.
*S.G. Sharapov* - The theory is developed for sound waves emitted by Au, Ag and Cu nanoparticles embedded in the plexiglass matrix under ultrashort laser pulses irradiation. Analytical expressions are obtained for the amplitude and power of the longitudinal spherical acoustic oscillations as functions of density and elastic properties of the medium, the laser pulse duration, electron temperature, particle radii, and electron-phonon coupling constant. The factors affecting the dynamics of the power damping of these waves are studied in detail.
*N.I. Grigorchuk*

Department for Computational Methods in Theoretical Physics

- The model of migration processes in the crystalline matrix of cadmium iodide with isomorphic lead iodide nanoinclusions has been developed. Stoichiometric effect on the processes of charge carrier trapping has been analyzed. It was found that one of the possible mechanisms of photoelectret state formation in this system is associated with orientational polarization of nonlinear lead iodide molecule.
*N.V. Gloskovska* - We present a broad palette of discussions of the concepts of a molecule and a chemical bond that always lay down behind all computational modeling in quantum chemistry and of the endohedral fullerene He
_{2}@С_{60}in particular. For this purpose, we offer the definition of quantum chemistry as composed of three ingredients. Each of them is illustrated by its particular concept, either that of a molecule or a bond. The third, computational ingredient is tackled to resolve the bonding manifold of He_{2}@С_{60}*E.S. Kryachko* - The thermoelectric properties of molecular nanostructures have been investigated. The mechanism of transport in these structures associated with electron tunneling has been explained. The Seebeck coefficient for such structures is found to be in good agreement with experiment. It is shown that thermoelectric effects in these nanostructures can be enhanced by changing some parameters.
*V. Ermakov, S.P. Kruchinin* - A mechanism of regulation of enzymatic activity has been proposed. It is alternative to allostery since it does not require the interaction between spatially separated binding sites and is of purely kinetic nature. As distinct from the classical allostery schemes in which the regulation amplitude is restricted by the degree of oligomery of the enzyme, the kinetic mechanism provides much more enhanced control possibilities by means of simply changing the relation between the times of the turnover of the enzyme and its structural relaxation. The existence of such apparent "allostery" and its physiological importance have been recently proved experimentally, see PNAS USA, 112, 11430 and 11553, Sept 15, 2015
*L.N. Christophorov*

Department for Applied Problems in Theoretical Physics

- The structure of the mirror nuclei
^{14}С and^{14}O is studied within a five-particle model (three alpha-particles plus two extra nucleons). The interaction potentials are proposed to have data fit with the experimental energy and radius of^{14}С nucleus, as well as with the energy of^{14}O. Within the variational approach in Gaussian representation, we obtain the ground state wave functions of the abovementioned five-particle systems. The charge r.m.s. radius of^{14}O nucleus is predicted. The charge density distributions and elastic formfactors are found.*B.E. Grinyuk, D.V. Piatnytskyi* - Some quasi-relativistic equations are found to have similar expansions in 1/c up to the fourth order to within the terms removable by additional unitary transformations. The expansions of these equations contain only the terms proportional to е
^{2}, while expansions of the Breit and Salpeter equations contain the terms ~ е^{4}.*A.I. Turovsky*

Department for Synergetics

- The superconductivity model wherein the energy gap is asymptotically tending to zero with decrease of temperature or magnetic field has been proposed. Formally, both critical temperature and magnetic field for such a superconductor are infinite ones. The free energy functional has been obtained and Ginzburg-Landau theory for such a superconductor has been developed. A simple quasi-classical statistical model for the description of electrons on a liquid-helium surface in an external electric field is proposed.
*A.G. Zagorodny, B.I. Lev, K.V. Grigorishin, V.B. Tymchyshyn* - The energy interaction between colloidal particles with arbitrary shapes and sizes in nematic liquid crystal with different elastic Franck constants has been obtained The difference between elastic constants can lead to both quantitative and qualitative changes of interparticle potential. The probability of the linear chain formation by colloidal particles of in nematic liquid crystal with buckling constant has been theoretically predicted.
*O.M. Tovkach, B.I. Lev* - The metabolic process of glycolysis arising as a product of the biochemical evolution in protobionts has been studied by means of the mathematical model. Conditions of self-organization of the given process have been searching into the dissipative structure theory. The phase-parametric diagrams of a cascade of bifurcations which characterize the transition to chaotic modes according to the Feigenbaum scenario and the intermittence have been constructed. The strange attractors formed as a result of the funnel effect have been found. The complete spectra of Lyapunov indices and divergences for the obtained modes are calculated. The values of KS-entropy, predictability horizons, and Lyapunov dimensions of strange attractors have been determined.
*V.I. Grytsay*

Department for Structure of Atomic Nuclei

- We present a phase-space representation of quantum state vectors for two-cluster systems. Density distributions in the Fock-Bargmann space are constructed for bound and resonance states of
^{6;7}Li and^{7;8}Be, provided that all these nuclei are treated within a microscopic two-cluster model. The input parameters of the model and nucleon-nucleon potential were selected to optimize description of the internal structure of clusters and to reproduce position of the ground state with respect to the two-cluster threshold. The dominant two-cluster partition of each nucleus was taken into consideration. The density distribution in the phase space is compared with those in the coordinate and momentum representations. Bound states realize themselves in a compact area of the phase space, as also do narrow resonance states. We establish the quantitative boundaries of this region in the phase space for the nuclei under consideration. Quantum trajectories are demonstrated to approach their classical limit with increasing energy.*Yu.A. Lashko, G.F. Filippov, V.S. Vasilevsky* - General properties of resonance states of light nuclei that disintegrate into three cluster particles and do not disintegrate into two particles are studied in terms of a model that employs a basis of hyperspherical functions and thus provides implementing proper boundary conditions. It is established, that the increase of coupling between channels leads to the decrease of resonance energy. At certain values of the constant, responsible for coupling of channels, resonance states transform into bound states. It is shown, that narrow resonance states can exist with weak and strong coupling between channels. As a rule, energy and width of resonance states are decreasing when number of open channels is increased. There is large probability, as is established, to observe super narrow resonance state with large number of open channels. It is also demonstrated, that resonance states are formed and decay only in very restricted number of channels of three-cluster continuum. The simple model reproduces general properties of three-cluster systems, which were obtained in realistic three-cluster model.
*V.S. Vasilevsky*

Department for Theory and Simulation of Plasma Processes

- A nonlinear model of a scalar field coupled to its gradient has been proposed. The model is shown to be suitable for the description of phase transitions accompanied by the formation of spatially inhomogeneous distributions of the scalar field in the ground state. Some solutions of the proposed model have been obtained; these can be related, e.g., to the cosmological scenario or the spinodal decomposition. The proposed model is analogical to the mechanical nonlinear oscillator with coordinate-dependent mass or velocity-dependent elastic modulus. This analogy is employed to reveal the existence of limit cycles and destruction of new phase bubbles.
*A.G. Zagorodny, B.I. Lev* - The superconductivity model wherein the energy gap is asymptotically tending to zero with decrease of temperature or magnetic field has been proposed. Formally, both critical temperature and magnetic field for such a superconductor are infinite ones. The free energy functional has been obtained and Ginzburg-Landau theory for such a superconductor has been developed. A simple quasi-classical statistical model for the description of electrons on a liquid-helium surface in an external electric field is proposed.
*A.G. Zagorodny, B.I. Lev, K.V. Grigorishin, V.B. Tymchyshyn* - We apply the reductive perturbation method to the simple electrostatic ion-temperature-gradient mode in an advanced fluid description. The fluid resonance turns out to play a major role for the excitation of zonal flows. This is the mechanism recently found to lead to the low-to-high (L-H) mode transition and to the nonlinear Dimits upshift in transport code simulations. It is important that we have taken the nonlinear temperature dynamics from the Reynolds stress as the convected diamagnetic flow. This has turned out to be the most relevant effect as found in transport simulations of the L-H transition, internal transport barriers and Dimits shift. This is the first time that an analytical method is applied to a system which numerically has been found to give the right experimental dynamics.
*A.G. Zagorodny* - The approach we proposed earlier for description of particle diffusion in two-dimensional random velocity field has been compared with the decorrelation trajectory method. A frozen turbulence as the most difficult test for the statistical theories has been considered. Different statistical closures of equations for averaged quantities were compared, and validity of subensemble concept was analyzed analytically and numerically to formulate the approach that combines advantages of both methods.
*O.M. Cherniak*

Department for Theory of Nuclei and Quantum Field Theory

- We study the influence of a background magnetic field and boundary conditions on the vacuum of a quantized charged spinor matter field in a bounded space. It is found that, in the case of a sufficiently strong magnetic field directed orthogonally to two parallel bounding plates, the Casimir force is independent of a boundary condition, as well as of the distance between the plates.
*Yu.A. Sitenko* - New analytical expressions for the p-, d- and f-wave partial two-body Coulomb transition matrices at the energy of the ground bound state of the complex have been derived. The obtained results have been used for studies of the properties of few-body atomic and nuclear systems.
*V.F. Kharchenko* - By making use of the recommended proton-proton low-energy interaction parameters the following value for the charged pion-nucleon coupling constant has been obtained. The calculated value of this quantity appears to be in excellent agreement with the experimental result of the Uppsala Neutron Research Group.
*V.A. Babenko, N.M. Petrov*

Department for Computer Maintenance

- The highly reliable cloud infrastructure under control OpenStack system has been built on the base of computing cluster of the Bogolyubov Institute for Theoretical Physics of the NAS of Ukraine. BITP cloud infrastructure is the first Ukrainian cloud resource which has been integrated in the EGI Federal Cloud. The integration of BITP cloud infrastructure to CERN cloud infrastructure has been done to perform of data processing of ALICE experiment.
*S.Ya. Svistunov* - Highly accurate numerical simulations are employed to highlight the subtle but important differences in the mechanical stability of perfect crystalline solids versus amorphous solids. We stress the difference between strain values at which the shear modulus vanishes and strain values at which a plastic instability ensues.
*V.V. Dailidonis*