Bogolyubov Institute for Theoretical Physics
of the National Academy of Sciences of Ukraine

Department of 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
  • The spin Hall conductivity and thermo-spin coefficient is calculated for silicene -a bright representative of Dirac materials. It is shown that the standard Kubo formalism has to be altered by including the effective magnetization in order to satisfy the third law of thermodynamics. A strong spin Nernst effect (spintronic analog of the usual Nernst-Ettinghausen effect) with nontrivial dependences on the carrier concentration and electric field applied is predicted to exist in silicene and other low-buckled Dirac materials.
    V.P. Gusynin, S.G. Sharapov
  • We identify a weak line at E ~ 3.5 keV in X-ray spectra of the Andromeda galaxy, the central part of our Galaxy and the Perseus galaxy cluster - the dark matter-dominated objects, for which there exist deep exposures with the XMM-Newton X-ray observatory. Such a line was not previously known to be present in the spectra of galaxies or galaxy clusters. Although the line is weak, it has a clear tendency to become stronger towards the centers of the objects; it is stronger for the Perseus cluster than for the Andromeda galaxy and is absent in the spectrum of a very deep "blank sky" dataset. Although for individual objects it is hard to exclude the possibility that the feature is due to an instrumental effect or an atomic line of anomalous brightness, it is consistent with the behavior of a line originating from the decay of dark matter particles. The dark matter interpretation of the signal observed in Perseus galaxy cluster and Andromeda galaxy is fully consistent with these data. Future detections or non-detections of this line in multiple astrophysical targets may help to reveal its nature.
    D.A. Iakubovskyi
  • Rhombohedral multilayer graphene together with Bernal stacked bilayer graphene belongs to a new class of chiral two-dimensional electron systems characterized by the low energy Hamiltonian with chiral properties. The dynamical polarization function is calculated in the neutral rhombohedral multilayer with dynamically generated gap. Taking it into account, a self-consistent gap equation is derived whose solutions show that the gap is maximal in rhombohedral trilayer graphene. It is shown that the gap monotonously decreases with subsequent increase of the number of layers due to the fact that the effects of screening win over those connected with the decrease of curvature of the electron energy zones.
    V.P. Gusynin, E.V. Gorbar
  • The leading radiative corrections to the axial current in the chiral separation effect are calculated in dense QED in an external magnetic field. Although in the literature there are arguments related with the chiral anomaly which determine the axial current through the topological contribution in the lowest Landau level in the free theory, it was found that the quantum electrodynamical interaction leads to nontrivial radiative corrections to the axial current. The direct calculations performed to the linear order in the external magnetic field showed that the nontrivial radiative corrections to the axial current are provided by the Fermi surface singularity in the fermion propagator at nonzero fermion density.
    E.V. Gorbar
  • The confinement phase transition had a strong impact on the dynamics of the early universe. Witten noticed the possibility that part of the colored objects - quarks and gluons escape phase transition, remaining as islands of colored objects, called quark-gluon nuggets (quark nuggets - QN). We studied the evolution of the universe filled with QN, on a late period of its evolution, when inhomogeneities such as 1-t or 2-nd group galactic were already formed. In that late, nonlinear stage, the hydrodynamical approach is not applicable for the analysis. Instead, mechanical analogues were used. They describe phenomena inside the inhomogeneity cells, and provide a good means to study scalar excitations in various cosmological models. Compatibility of cosmological models containing QN with mechanical ones was proven. To do so, a model of the universe filled with dust (both baryon and dark matter), radiation and QN was studied. At a late period of the evolutions and at distances much smaller the inhomogeneity scales (about 190 Mps), our universe was strongly inhomogeneous. It is important to account for inhomogneneities in form of galactic, groups and clusters of galactic. We have assumed that radiation and QN fluctuate around some average values. These fluctuations, as well as the inhomogeneities violate the metrics, for which reason a mechanical method is preferable. It made possible to account for a small admixture of colored objects (QN) that survived after the phase transition.
    L.L. Jenkovszky
  • The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory can be reduced to the Einstein equations with an additional source of the gravitational field of quantum nature. After averaging over corresponding quantum states of the scalar field which plays the role of a surrogate of primordial matter, the classical source of the gravitational field takes the form of a barotropic fluid. The exact solution of the non-linear equation for the phase of the wave function in the model of the free scalar field is found and it is shown that the averaged free scalar field turns into the Weyssenhoff spin fluid. In the semi-classical approximation, the obtained equations coincide with the equations of the Einstein-Cartan theory. The cases when the contribution of the quantum effects into the gravitational interaction becomes significant on macroscopic scale are analyzed. It is demonstrated that, unless the whole, at least a part of such matter-energy constituents as dark matter and dark energy may have a quantum origin.
    V.V. Kuzmichev
  • We review the current status of indirect search for dark-matter signatures in gamma-rays including the recently claimed line candidate at ~130 GeV. To resolve the origin of this line candidate (instrumental, astrophysical, decay/annihilation of dark-matter particles), we propose special observations of the Galactic Center using the future gamma-ray mission Gamma-400.
    D.A. Iakubovskyi, D.I. Malyshev
  • We show that the current bounds on the decaying dark matter in keV region can be significantly improved using Large Observatory For X-ray Timing (LOFT) - a next-generation X-ray telescope selected by the European Space Agency as one of the space mission concepts within the "Cosmic Vision" programme with the launch possibility in the beginning of 2020th. Using special simulations that take into account the existing (Requirement) and future (Goal) characteristics of the Large Area Detector (LAD), we show that the current bounds on the decaying dark matter can be improved 10-30 times in the 1.5-30 keV range. This not only makes LOFT suitable for a number of pure astrophysical problems but also allows one to probe an interesting range of parameters of particle physics beyond the Standard Model not accessible to any other existing and planned ground and cosmic-based experiment.
    D.A. Iakubovskyi
  • Using the observations of the Fermi Gamma-ray Space Telescope, we performed measurements and obtained upper limits on the emission of Cyg X-1 in the photon energy range of 0.03-300 GeV. The results are presented separately for the hard and soft spectral states of the source. In the hard state, we detected a weak steady emission in the 0.1-10 GeV range with a power-law photon index of Γ ? 2.6 ± 0.2. This measurement, even if considered to be an upper limit, strongly constrains Compton emission of the steady radio jet, present in that spectral state. If optically thin synchrotron emission of the jet is to account for the MeV tail, the value of the magnetic field in the jet has to be much above equipartition. The GeV-range measurements also strongly constrain models of hot accretion flows, most likely present in the hard state, in which γ-rays originate from the decay of neutral pions produced in collisions of energetic ions in the inner part of the flow. In the soft state, the obtained upper limits constrain electron acceleration in a non-thermal corona, present around the accretion disc. The coronal emission above 30 MeV has to be rather weak, which is most readily explained by absorption of γ-rays in pair-producing photon-photon collisions. Then, the size of the bulk of the corona is less than a few tens of the gravitational radii.
    D.I. Malyshev
  • We analyzed broad multi-wavelength observations of the 2010-2011 periastron passage of the gamma-ray loud binary system PSR B1259-63. High-resolution interferometric radio observations establish extended radio emission trailing the position of the pulsar. Observations with the Fermi Gamma-ray Space Telescope reveal GeV gamma-ray flaring activity of the system, reaching the spin-down luminosity of the pulsar, around 30 days after periastron. There are no clear signatures of variability at radio, X-ray and TeV energies at the time of the GeV flare. Variability around periastron in the Hα emission line can be interpreted as the gravitational interaction between the pulsar and the circumstellar disk. The equivalent width of the Hα grows from a few days before periastron until a few days later, and decreases again between 18 and 46 days after periastron. In near infrared, we observe the similar decrease of the equivalent width of Brγ line between the 40th and 117th day after the periastron. For the idealized disk, the variability of the Hα line represents the variability of the mass and size of the disk. We discuss possible physical relations between the state of the disk and GeV emission under assumption that GeV flare is directly related to the decrease of the disk size.
    D.I. Malyshev
  • We studied the properties of the diffuse γ-ray background around the Galactic plane at energies 20-200 GeV. We found that the spectrum of this emission possesses significant spatial variations with respect to the average smooth component. The positions and shapes of these spectral features change with the direction on the sky. We therefore, argue that the spectral feature around 130 GeV, found in several regions around the Galactic Center and in the Galactic plane, cannot be interpreted with confidence as a γ-ray line, but may be a component of the diffuse background and can be of instrumental or astrophysical origin. Therefore, the dark-matter origin of this spectral feature becomes dubious.
    D.I. Malyshev
  • An all-sky X-ray map in hard X-rays (2-10 keV) is built with detailed treatment of systematic errors. The resulting maps in hard X-rays (XMM-Newton) and gamma-rays (Fermi) are located at a specially adapted public web interface of the VIRGO observatory at
    D.I. Malyshev, D.O. Savchenko, D.A. Iakubovskyi
  • The Bose-Einstein condensation (BEC) of magnons created by a strong pumping in ferromagnetic thin films of yttrium iron garnet used as systems of finite size is considered analytically. Such a peculiarity, typical for this magnetic material, as the presence of a minimum in the spectrum of spin waves at a finite value of the wave vector is taken into account. The definition of high temperature BEC is introduced and its characteristics are discussed. A role of boundary conditions for spin variables is analyzed, and it is shown that in the case of free spins on the boundary the magnon lattice can form in the system. The factors responsible for its appearance are discussed.
  • Free energy for Z(2) and Z(3) spin systems is calculated as a finite sum in relations of an iterated main eigenvalues of the transfer matrix. For the Ising model on the lattice strip of the width M=16 it is shown to be practically indistinguishable from an exact one already after 5 renormalization group (RG) iterations. Z(4) and Z(5) spin systems are investigated within the modified phenomenological RG framework. For the Z(5) model, the phase structure in the full range of the coupling constants (t1 [0,1], t2 [0,1]) is analyzed. Four fixed points'positions are found. These fixed points correspond to: 1) the standard Potts model (t1 = t2); 2) the vector Potts model where t1 and t2 relate to each other by certain parametrical dependency; 3) and 4) an extra fixed points t1 = 0.589, t2 = 0.053 and its symetric counterpart t2 = 0.589, t1 = 0.053. It is shown that the critical exonent ν in these extra fixed points tends to infinity as the lattice strip's width M increases which means these points correspond to phase transition of an infinite order. The phase flow in the vicinity of the fixed points is analyzed. Obtained approximate results reproduce an exact ones with very good precision whenever these last are available.
    V.A. Kushnir
  • We have found that the boundaries affect strongly the bulk microstructure of helium-II. In particular, the formulas for the phonon energy and the ground-state energy of a system with boundaries differ from those of a closed system by the factor outside the interatomic potential (here, d is the number of noncyclic coordinates).
    M.D. Tomchenko
  • We propose a novel approach to the problem of boundary conditions for scalar cosmological perturbations in a braneworld model. It consists in considering the topology of a spatially closed universe that bounds a compact set in the four-dimensional space. This space does not have any boundaries except for the brane itself; the setup is thus characterized as a multi-dimensional theory without boundaries (no-boundary). It is shown that equations for scalar perturbations effectively close on the brane in this approach if its spatial curvature is marginally small. A new additional modes of the evolution of perturbations of matter density are found, the presence of which in principle distinguishes this model from the standard cosmology based on general relativity.
    A.V. Viznyuk, Yu.V. Shtanov
  • We estimated the residual magnetic field on superlarge spatial scales in the inflationary scenario in a marginally open universe. It is shown that the expected magnitude of the magnetic field on scales larger than the scale of spatial curvature cannot exceed 10-59 G in this scenario.
    Yu.V. Shtanov
  • Classical solutions of the O(3) nonlinear sigma model with the parametrization of S2 sphere by orthogonal wave vectors (lattice) are found. The solutions of a set of differential equations reduce to the Liouville, sin- and sinh- Gordon equations through the Belavin-Polyakov self-dual equations. The solutions of wave-crystal type are presented also for the SO(5) nonlinear sigma model which serves as a model for high temperature superconductivity. We constructed conformal gauge- invariant tensor conservation laws for abelian p-forms gauge theory and Yang conformal gravity as bilinear forms being Hodge dual to strengths of fields and Killing conformal fields. These tensor currents exist in critical space-time dimensions where the energy-momentum tensor is traceless.
  • We investigated the Casimir effect for charged scalar matter in a constant and homogeneous external magnetic field. In a general case, we obtained final expressions for the surface vacuum energy density and pressure at the boundary. We consider the asymptotic behavior of the vacuum-energy density and pressure in the cases of strong and weak external magnetic field. It was proved that the vacuum energy density is practically independent of the details of the boundary conditions in the case of a strong magnetic field.
    Yu.A. Sitenko, S.А. Yushchenko
  • A reggeometric (Regge+geometry) model of lepton-hadron and hadron-hadron processes was developed. The new features of the model are: a) two different classes of reactions are considered on the same footing, and b) the number of the free parameters is limited, being the same in different classes of reactions: deeply-virtual Compton scattering (DVCS), exclusive diffractive production of vector mesons and in elastic hadron scattering.
    L.L. Jenkovszky
  • Chiral asymmetry of the normal ground state was investigated in quantum electrodynamics at nonzero fermion density in an external magnetic field. The electron self-energy in a magnetized QED plasma to the leading perturbative order in the coupling constant and to the linear order in an external magnetic field was calculated. It is found that the chiral asymmetry of the normal ground state of the system is characterized by two new Dirac structures. One of them is the familiar chiral shift previously discussed in the Nambu--Jona-Lasinio model. The other structure is new. It formally looks like that of the chiral chemical potential, but is an odd function of the longitudinal component of the momentum, directed along the magnetic field. The origin of this new parity-even chiral structure is directly connected with the long-range character of the QED interaction. The form of the Fermi surface in the weak magnetic field is determined.
    E.V. Gorbar
  • The phase diagram of a Dirac semimetal in a magnetic field at a nonzero charge density was studied. It is shown that there exists a critical value of the chemical potential at which a first-order phase transition takes place. At subcritical values of the chemical potential the ground state is a gapped state with a dynamically generated Dirac mass and a broken chiral symmetry. The supercritical phase is the normal (gapless) phase with a nontrivial chiral structure: it is a Weyl semimetal with a pair of Weyl nodes for each of the original Dirac points. The nodes are separated by a dynamically induced chiral shift. The direction of the chiral shift coincides with that of the magnetic field and its magnitude is determined by the strengths of the magnetic field, the quasiparticle charge density, and the strength of the interaction.
    E.V. Gorbar