List of Departments
Topmost Scientific Results

- Department of Astrophysics and Elementary Particles
- Department of High-Density Energy Physics
- Department of Theory of Quantum Processes in Nanosystems
- Department of Mathematical Methods in Theoretical Physics
- Department of Theory of Nonlinear Processes in Condensed Matter
- Department of Synergetics
- Department of Theory of Nuclei and Quantum Field Theory
- Department of Computer Maintenance

Department of High-Density Energy Physics

- Using the method of molecular dynamics, the effect of the liquid-gas mixed phase on fluctuations in the number of particles was investigated. The metastable region of the mixed phase is modeled as a system of non-interacting clusters. Large fluctuations were detected in the region of spinodal instability.
*M.I. Gorenstein, R.V. Poberezhnyuk, O.V. Savchuk* - In a simple analytically solvable model of the thermal expansion system, two-boson momentum correlations were investigated with a fixed limitation of the number of particles in proton-proton collisions at energies characteristic of the Large Hadron Collider. It is shown that an increase in the rate of expansion, as well as an increase in the multiplicity of particles, increases the contribution of the ground state to the momentum spectra of particles and leads to the suppression of the Bose-Einstein momentum correlation. These conclusions are directly related to the recently experimentally discovered dependence of the Bose-Einstein momentum correlation on the multiplicity.
*Y.M. Sinyukov, M.D. Adzhimambetov, S.V. Akkelin* - An exact solution is obtained for a wide class of models of Polyakov loops on a lattice in arbitrary dimensions with gauge groups U(N) and SU(N) in the limit when the number of colors (
*N*) and the number of quark flavors (*N*) go to infinity. Analytical expressions for the shielding chromoelectric and chromomagnetic masses of gluons in the deconfinement phase were obtained. It was found that in a certain range of parameters in the deconfinement phase, the correlation functions have an exponential decline modulated by the oscillatory functions. This means that the chromoelectric masses are complex._{f}*O. Borisenko, V. Chelnokov, S. Voloshin* - A model of the star as a system of pi mesons in the Bose condensate state is formulated. Calculated mass-radius ratios for the pi-meson part and parameters of its lepton environment.
*M.I. Gorenstein, O. Savchuk* - A dual representation for SU(N) gauge theories with dynamical quarks is constructed. This representation was used for numerical Monte Carlo simulations of the effective Polyakov loop model at finite baryon density. Various local observables such as energy density, baryon density, quark condensate were calculated and the phase diagram of the model was detailed.
*O. Borisenko, S. Voloshin* - Two mysterious femtoscopic observations in collisions of ultrarelativistic heavy ions are considered in detail. First, it is the proximity of the maximum times of pion emission at completely different collision energies: from the highest energies of RHIC to the upper energies of LHC. Another paradoxical effect is that, despite the rather long duration of the post-hydrodynamic cascade stage, the times of maximum emission observed are close to the times of particleization - the transformation of the quark-gluon liquid into hadrons. A detailed analysis of the features of the hydrodynamic evolution of the system at different energies of the colliding nuclei and the structure of the emission function of pions and kaons in the hadronic stage sheds light on these paradoxical results.
*Y.M.Sinyukov, M.D. Adzhimambetov, S.V. Akkelin*

- A system of bosons studied within the mean-field framework has two fascinating phenomena: a liquid-gas first order phase transition and Bose-Einstein condensation. Depending on the mean-field potential parameters one can observe two types of critical points (CP), that belong to different universality classes with distinct sets of critical exponents. As examples the pion and α matter are considered.
*V. Kuznietsov, O. Savchuk, and M.I. Gorenstein* - Two-boson momentum correlations at fixed particle number constraint are studied in a simple analytically solvable model of a thermal expanding system. It was shown that the increase of expansion rate, as well as increase of particle multiplicity, enhances the ground-state contribution to particle momentum spectra and leads to suppression of the Bose-Einstein momentum correlations. These findings are directly related to the recently found phenomena as for multiplicity-dependence of the Bose-Einstein momentum correlations in high-multiplicity p+p collision events at the LHC.
*M.D. Adzhymambetov, S.V. Akkelin, Yu.M. Sinyukov* - An exact solution is obtained for a wide class of Polyakov loop models on a lattice in arbitrary dimension with U(N) and SU(N) gauge groups in the limit when N and Nf go to infinity, where N is the number of colors, and Nf is the number of quark flavors. This made it possible to obtain analytical expressions for screening chromo-electric and chromo-magnetic masses of gluons in the deconfinement phase. It was also established that in a certain region of parameters in the deconfinement phase the exponential decay of correlation functions is modulated by an oscillating function. This means that the chromo-electric masses are complex.
*O. Borisenko, V. Chelnokov, S. Voloshin* - A model of the vertex of three-Froissarton interaction has been constructed, which provides small corrections to the original Dyson-Schwinger equation and allows to solve the problem of breaking unitarity in the diffraction production of many massive hadron beams (the Finkelstein-Kajanti problem).
*E. Martynov, G. Tersimonov*

- The analysis of parton scattering is performed taking into account multiparton distribution functions. The properties of these functions are investigated. The obtained results provide new unique information about the structure of hadrons and the dynamics of their interaction.
*Cor.-member of the NAS of Ukraine G.M. Zinoviev* - The equation of state for the interacting pi-meson system that includes the Bose-Einstein condensation and first order phase transition was obtained. The search for such physical systems by measuring the electric charge fluctuations was proposed.
*M.I. Gorenstein, R.V. Poberezhnyuk, O.V. Savchuk* - Two-particle momentum correlations in the system of N identical bosons are studied on the basis of a quantum canonical ensemble. New effects related to high-temperature Bose-Einstein condensation of pions in small systems are identified.
*Y.M. Sinyukov, M.D. Adzhymambetov, S.V. Akkelin* - Using variational principle, we show that a condition of the spatial collapse in imperfect Bose gas is absolutely not determined either by the value or by the sign of the scattering length, in the contrary to the result following from the Gross-Pitaevskii equation, where the collapse is predicted at negative scattering length.
*B.E. Grinyuk, K.A. Bugaev*

- The integrated Hydrokinetic Model is updated by incorporating the additional mechanisms of photon radiation to analyze the spectra of direct photons, as well as elliptic and triangular flows at energies of nuclear collisions at colliders RHIC and LHC for various collision centralities. It was found that the selfconsistent description of these data requires the inclusion of photon radiation associated with confinement processes ("hadronization photons") and entanglement effects.
*Cor. Member of the NAS of Ukraine G.M. Zinovjev, Yu.M. Sinyukov* - New formalism of self-consistent treatment of whole excluded volume of the mixture of hadrons with an arbitrary number of hard-core radii and such clusters as light (anti-, hyper-) nuclei is suggested. It was possible to derive a realistic equation of state for such mixtures that allows one to go beyondthe Van der Waals approximation. Deaing wth new equation of state, we developed hadron resonance gas model providing the very accurate description of multiplicities of hadrons and nuclei measured in the central nuclear collisions by the ALICE CERN Collaboration at the center-of-mass 2760 GeV and by the STAR BNL Collaboration at 200 GeV.
*Cor. Member of the NAS of Ukraine G.M. Zinovjev, K.O. Bugaev, B.E. Grinyuk, V.V. Sagun, O.I. Ivanytskyi* - It is developed the subensemble acceptance method that quantifies the effect of global conservation laws and is an important step toward a direct comparison between cumulants of conserved charges measured in central heavy ion collisions and theoretical calculations of grand-canonical fluctuations, such as lattice QCD. As an example, we apply our formalism to net-baryon fluctuations at vanishing baryon chemical potentials as encountered in collisions at the LHC.
*R.V. Poberezhnyuk, M.I. Gorenstein* - Using the Laplace-Fourier transformation technique, the method to exactly account for the particle number fluctuations for the equations of state with induced surface and curvature tensions is suggested. Such an approach allows one to generalize the classical concept of morphological thermodynamics to the dense mixtures of both the Boltzmann particles and the quantum ones with the hard-core repulsion. In contrast to the standard formulation, in the new approach the coefficients of induced surface and curvature tensions are suppressed at hight densities not by the exponential, but by the power-like functions of system pressure.
*K.O. Bugaev* - Simultaneous effects of finite system size and global charge conservation on thermal fluctuations in the vicinity of a critical point are investigated. A finite interacting system that exchanges particles with a finite reservoir (thermostat) is considered. It is shown that such a statistical ensemble differs from the common canonical and grand canonical ensembles, and global charge conservation effects strongly influence the cumulants of particle number distribution. If the system size is sufficiently large, the global charge conservation effects can be accurately described analytically within a recently developed subensemble acceptance method. It is found that the finite size effects start to play a significant role when the correlation length grows large due to the proximity of the critical point or when the system is small enough to be comparable to an eigenvolume of an individual particle.
*R.V. Poberezhnyuk., М.І. Gorenstein*

- 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.
*Cor. 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*

- The equation of state with the induced surface tension is generalized to quantum gases with the mean-field interaction. Such an approach allows one to go beyond the Van der Waals approximation for quantum systems. Explicit expressions for the quantum virial coefficients of arbitrary order are found in the low density limit. All virial coefficients for the quantum Van der Waals equation of state are found as well.
*K.A. Bugaev, A.I. Ivanytskyi, V.V. Sagun, corr. member of NAS of Ukraine G.M. Zinovjev* - The spectrum of photons with large transverse momentum is calculated and compared with the experimental data within the framework of the model of synchrotron radiation, which results from quark interactions with the collective confining color field in relativistic heavy ion collisions. It makes it possible to demonstrate the feasibility of this type of radiation due to distinctive features of lepton pair production in the corresponding experiments.
*corr. member of NAS of Ukraine G.M. Zinovjev* - On the basis of Froissaron and Maximal Odderon model for proton and antiproton interaction at zero transferred momenta it is shown that the latest data of the TOTEM experiment at CERN give evidence for the discovery of odderon contribution, which was predicted almost 50 years ago. Moreover, the generalization of the model for differential cross-sections of nucleon elastic scattering confirmed the presence of odderon effects in the interaction of high-energy protons and antiprotons at non-zero transferred momenta.
*E.S. Martynov* - Statistical model of quark-gluon bags with a continuous transition to the high temperature phase is developed. Thermodynamical functions and fluctuations of conserved charges are calculated. The results are in agreement with those obtained within QCD lattice calculations.
*M.I. Gorenstein* - Within the framework of the evolution model of high ion collisions at LHC energies it is found that the inelastic reactions after matter hadronization influence on the relation of different particle number formation. Such reactions are important (compensated) factor of the hadron production, which restricts a direct studying the equation of quark-gluon plasma state and initial conditions of superdense matter formation.
*Yu.M. Sinyukov, V.M. Shapoval*

- 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 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 = 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*

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