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

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Department of Mathematical Methods in Theoretical Physics

Deputy head of department – Prof., Dr. Oleksandr M. Gavrilik.

The department incorporates the Laboratory of Integrable Systems.
Head of the laboratory – Dr. Nikolai Z. Iorgov.

Research fields
  • Symmetry theory: methods of the theory of groups, their representations, and physical applications
  • Quantum groups, quantum algebras, quantum homogeneous spaces
  • Group representations theory and special functions
  • Theory of integrable systems
  • Classical and quantum field theory
  • Theory of elementary particles
Alexandre M. Gavrilik
Position: Head of the Department
Dr.
Prof.
omgavr@bitp.kiev.ua
Alexander V. Zolotaryuk
Position: Chief Researcher
Dr.
azolo@bitp.kiev.ua
Taras Volodymyrovych Skrypnyk
Position: Leading Researcher
Dr.
tskrypnyk@bitp.kiev.ua
Andriy V. Nazarenko
Position: Leading Researcher
Dr.
nazarenko@bitp.kiev.ua
Yuri A. Mishchenko
Position: Researcher
Ph.D.
mishchenko@bitp.kiev.ua
Maria V. Khelashvili
Position: Leading Engineer
mary.khelashvili@gmail.com
Ostap P. Mykhailiv
Ph.D. Student
ostappolitics1994@gmail.com
Laborarory of Theory of Integrable Systems
Nikolai Z. Iorgov
Position: Head of the Laboratory
Dr.
iorgov@bitp.kiev.ua
Yuri I. Bespalov
Position: Researcher
Ph.D.
yu.n.bespalov@gmail.com
Yuri V. Tykhyy
Position: Researcher
Ph.D.
tykhyy@bitp.kiev.ua
Yurii S. Zhuravlov
Position: Leading Engineer
Ph.D. Student
ujpake@gmail.com
Eduard E. Naichuk
Ph.D. Student
eduardnaich@gmail.com
Oleksii V. Yanchyshen
Ph.D. Student
oleksij.yanchyshen@gmail.com
  • Within the dark matter model based on the Gross-Pitaevski equation for a Bose-Einstein condensate with three-particle interaction, it is shown that at zero temperature the two- and three-particle correlations of the local density (averages of density products) indicate a first-order phase transition and reduce to the product of single-particle averages, as in an ideal gas, with increasing pressure. The time instability of two- and three-particle complexes is qualitatively described by quantum random walks between bound and unbound states. It is shown that the equations of chemical kinetics also admit the existence of complexes formed by dark matter particles with a long scattering length.
    A.M. Gavrilik, A.V. Nazarenko
  • Two approaches are developed for the study of the bound states of a one-dimensional Dirac equation with the potential consisting of multiple delta-function centers. One of these uses the Green's function method. The second approach is based on multiplying the one-center connection matrices and the free transfer matrices between neighbor centers. Within both these approaches, the transcendental equations for bound state energies are derived, the solutions to which depend on the strength of delta-centers and the distance between them. The principle of strength additivity is analyzed in the limits as the delta-centers merge at a single point or diverge to infinity.
    A.V. Zolotaryuk, V.P. Gusynin, O.O. Sobol, and Y. Zolotaryuk
  • Effective form factors for one-dimensional lattice fermions with arbitrary phase shifts were introduced. Tau functions defined as series ізf these form factors were studied. On the one hand, the exact summation was performed and tau functions as Fredholm determinants in the thermodynamic limit were presented. On the other hand, simple expressions of form factors allow to present the corresponding series as integrals of elementary functions. Using this approach the asymptotics of static correlation functions of the XY quantum chain at finite temperature were rederived.
    O. Gamayun, N. Iorgov, Yu. Zhuravlov
  • We have obtained a new integrable fermion hamiltonian of the BCS-Richardson type which is an anisotropic deformation of the famous fermion hamiltonian of Richardson, and have found its spectra with the help of the modified Bethe ansatz.
    T.V. Skrypnyk
  • Bose-condensate dark matter model is extended by taking into account both two- and three-particle self-interactions. The existence of nontrivial two-phase structure and possibility of first order phase transition in the central part of the dark matter halo of dwarf galaxies is confirmed. For a particular dwarf galaxy, the rotation curves and the entropy of bipartite entanglement in the halo of its dark matter are obtained.
    A.M. Gavrilik, A.V. Nazarenko
  • Conditions under which a quantum particle can be described using classical quantities are studied. The wavefunction of a quantum particle submitted to a potential field for which all quantum effects vanish, even if Planck's constant is non negligible, is investigated. This problem is equivalent to the problem of the motion of a particle in a refringent medium. In these media, quantum particles have classical momenta, while their wave properties are described by the wave-optics equation. In the 1D case, the particle cannot be found in the region near the origin, since the index of refraction tends to infinity there. For the 3D case with central symmetry, the wave properties are determined by a function, that has a resonance of width of the order of the de Broglie wavelength.
    V.E. Kuzmichev, V.V. Kuzmichev
  • The method of the algebraic Bethe ansatz was developed for the case of certain non-skew-symmetric gl(n)⊗gl(n)-valued classical r-matrices with spectral parameters. The Gaudin and BCS-type models associated with these r-matrices have been constructed. The spectrum and the eigen-vectors of the corresponding quantum Hamiltonians have been found in terms of solutions of the Bethe-type equations
    T.V. Skrypnyk
  • The problem of variables separation is explored for the classical integrable hamiltonian systems possessing gl(n)-valued Lax matrices satisfying quadratic Maillet brackets with spectral-parameter dependent a-b-c-d tensors. In terms of the corresponding a-b-c-d tensors components a sufficient condition that guarantees, that the separating functions of Sklyanin, Scott and Gekhtman produce canonical coordinates, is formulated. In the important subclass of classical a-b-c-d algebras, namely the case of classical reflection equation algebras, the analogous sufficient condition is formulated using the corresponding r-s-matrices, what guarantees the canonicity of the constructed coordinates. For the case of gl(n)xgl(n)-valued trigonometric a-b-c-d tensors that satisfy the considered condition, we find a class of the Lax matrices for which the obtained set of canonical coordinates is complete.
    T.V. Skrypnyk
  • Equations for the scattering data and discrete spectrum were obtained for the one-dimensional Schroedinger equation with the piecewise-constant potential. The asymptotical three-scale method of squeezing the system to zero width has been developed. It has been shown that the boundary conditions in the singular point make sense only when the mutual divergence cancellation in the connection matrix is possible. Two types of the transcendental equations for the resonance sets have been derived.
    O.O. Zolotaryuk, Y.O. Zolotaryuk
  • The problem of variables separation is explored for the classical integrable hamiltonian systems possessing gl(n)-valued Lax matrices satisfying quadratic Maillet brackets with spectral-parameter dependent a-b-c-d tensors. In terms of the corresponding a-b-c-d tensors components a sufficient condition that guarantees, that the separating functions of Sklyanin, Scott and Gekhtman produce canonical coordinates, is formulated. In the important subclass of classical a-b-c-d algebras, namely the case of classical reflection equation algebras, the analogous sufficient condition is formulated using the corresponding r-s-matrices, what guarantees the canonicity of the constructed coordinates. For the case of gl(n)xgl(n)-valued trigonometric a-b-c-d tensors that satisfy the considered condition, we find a class of the Lax matrices for which the obtained set of canonical coordinates is complete.
    T.V. Skrypnyk
  • We explore the consequences of including the repulsive three-particle interaction in the model of Bose-condensate dark matter model or fuzzy dark matter. Based on properly modified Gross-Pitaevskii equation, the model is aimed to describe the distribution of dark matter particles in the highly dense regions, such as the galaxy core and/or the overlapping halos of colliding galaxies. From numerical solutions for wave function and density profile, main thermodynamical characteristics are calculated. We reveal the existence of two distinct phases of dark matter, in the core of halo, separated by instability region between two special values of compression acting in the model. Some implications of the existence of two phases and the related first-order phase transition are discussed.
    A.M. Gavrilik, A.V. Nazarenko, M.V. Khelashvili
  • Two families of point interactions with bound state energy are realized from a heterostructure composed of two parallel homogeneous layers in the limit as their width and the distance between them tend to zero simultaneously. Under certain conditions described by transcendental equations, a resonant-tunneling transmission of electrons through this limit structure is shown to occur. A particular example of the singular potential having the form of the derivative of the Dirac delta-function is generalized to a whole family of point interactions, for which a single bound state does exist, contrary to the widespread opinion on the non-existence of bound states in δ-like systems.
    A. Zolotaryuk, Ya. Zolotaryuk
  • 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 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
  • Within the doubly special relativity theory which bounds both the velocities of particles (by the speed of light) and their energies (by the Planck scale) a new rule of so-called κ-addition for particle energies is proposed. A κ-dependent Hamiltonian of the one-mode multi-photon (sub)system is introduced and employed, with different modes being regarded as independent, to consider the thermodynamics of the black-body radiation and to obtain main thermodynamic quantities using analytical tools of the mean-field approximation and numerical evaluations based on exact formulas. The entropy of a one-mode subsystem turns out to be finite (bounded), and likewise the total energy density of radiation. Most unusual result is the existence of threshold temperature above which radiation is present.
    A.M. Gavrilik, A.V. Nazarenko
  • A phenomenon of splitting (furcation) resonant tunneling under electron transmission through a plain layer in the form of a single delta-like barrier with at least one adjacent well located at non-zero sufficiently small distance has been observed. It is shown that in the zero-thickness limit of the heterostructure the detachment of a countable resonance curves from the background level occurs for certain critical value of the squeezing parameter.
    A.V. Zolotaryuk
  • The Fredholm determinant and series representation of the tau-function of the Fuji-Suzuki-Tsuda system and its multivariate extension were derived. It is a generalization to higher rank (N=2) of the results obtained for Painlevé VI and the Garnier system. With its use a direct isomonodromic proof of the AGT-W relation for c=N−1 was obtained.
    N. Iorgov
  • 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 WN-algebra with central charge c=N-1 is constructed. This construction uses different properties of conformal blocks of WN-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
  • Ideal D-dimensional Bose gas is considered in a trap (external potential) in more general case than in previous works, namely, for isotropic potential U(r) = Arn +Br-m, where A, B > 0. The momentum distribution function is obtained, as well as the total number of particles, critical temperature, condensate fraction and heat capacity. Both high and low temperature regimes are considered. Conditions for the existence of Bose-Einstein condensation in the form of certain relations on n, m and D are being obtained.
    A.M. Gavrilik, I.I. Kachurik, Yu.A. Mishchenko
  • The whole class of one-point interactions realized in the limit when the thickness of two- and three-layer planar heteostructures as well as the distance between them are infinitesimal. It is established that depending on the way of realization of this limit, in the tunneling of electrons, the phenomenon of furcation of isolated resonances into multi-valued sets takes place.
    A.V. Zolotaryuk
  • We study symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are considered to be fixed different. The probability to find a walker at the given position and time is derived analytically. The probability distribution function is found: it has non-Gaussian form because of the properties of adsorption in the bulk of zones and reflection at the separation points. Time dependence of the mean squared displacement of a walker is also studied, and the anomalous behavior is revealed as compared with ordinary RW. Analytical calculation is in agreement with the results of numerical modeling based on first principles.
    A.V. Nazarenko
Articles in journals, other publications
  1. A.M. Gavrilik, A.V. Nazarenko, Bose–Einstein condensate dark matter that involves composites. Universe 8(3) , 187 (2022).
  2. V.P. Gusynin, O.O. Sobol, A.V. Zolotaryuk, Y. Zolotaryuk, Bound states of a one-dimensional Dirac equation with multiple delta-potentials, Low Temperature Physics/Fizyka Nyzkykh Temperatur, V.48, No.12, pp. 1157–1168 (2022).
  3. O. Gamayun, N. Iorgov, Yu. Zhuravlev, Effective free-fermionic form factors and the XY spin chain, SciPost Phys. 10, 070 (2021).
  4. Yu. Zhuravlev, E. Naichuk, N. Iorgov, and O. Gamayun, Large-time and long-distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas, Phys. Rev. B 105, 085145 (2022).
  5. T. Skrypnyk, Anisotropic BCS-Richardson model and algebraic Bethe ansatz, Nuclear Physics B, 975, 115679 (2022).
  6. T. Skrypnyk, The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz, SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 18, 074 (2022).
  7. T .Skrypnyk, Anisotropic Z n-graded classical r-matrix, deformed An Toda-and Gaudin-type models, and separation of variables, Journal of Mathematical Physics, 63, 091702 (2022).
  8. T .Skrypnyk, On the general solution of the permuted classical Yang–Baxter equation and quasigraded Lie algebras, Journal of Mathematical Physics, 63, 033507 (2022).
  9. Y. Tykhyy, Finite orbits of monodromies of rank two Fuchsian systems, Analysis and Mathematical Physics 12, article id.122 (2022). https://doi.org/10.1007/s13324-022-00698-2
  10. Lyudmila Kovalchuk, Roman Oliynykov, Yuri Bespalov, Mariia Rodinko, Methods of ensuring privacy in a decentralized environment, Information Security Technologies in the Decentralized Distributed Networks, - Lecture Notes on Data Engineering and Communications Technologies, Vol. 115, Springer-Verlag, 2022, https://doi.org/10.1007/978-3-030-95161-0_1, pp. 1-32.
  11. Lyudmila Kovalchuk, Roman Oliynykov, Yuri Bespalov, Mariia Rodinko, Analysis and research of threat, attacker and security models of data depersonalization in decentralized networks, Information Security Technologies in the Decentralized Distributed Networks, - Lecture Notes on Data Engineering and Communications Technologies, Vol. 115, Springer-Verlag, 2022, https://doi.org/10.1007/978-3-030-95161-0_3, pp. 71-88.
  12. Lyudmila Kovalchuk, Roman Oliynykov, Yuri Bespalov, Mariia Rodinko, Cryptographic mechanisms that ensure the efficiency of SNARK-systems, Information Security Technologies in the Decentralized Distributed Networks, - Lecture Notes on Data Engineering and Communications Technologies, Vol .115, Springer-Verlag, 2022, https://doi.org/10.1007/978-3-030-95161-0_8, pp. 185-201.
  13. Lyudmila Kovalchuk, Roman Oliynykov, Yuri Bespalov, Mariia Rodinko, Comparative analysis of consensus algorithms using a directed acyclic graph instead of a blockchain, and the construction of security estimates of spectre protocol against double spend attack, Information Security Technologies in the Decentralized Distributed Networks, - Lecture Notes on Data Engineering and Communications Technologies, Vol.115, Springer-Verlag, 2022, https://doi.org/10.1007/978-3-030-95161-0_9, pp. 203-224.
Papers at conferences and seminars
  1. Yuri Bespalov, Lyudmila Kovalchuk, Hanna Nelasa, Roman Oliynykov, and Alberto Garoffolo, Game theory analysis of incentive distribution for prompt generation of the proof tree in zk-SNARK based sidechains, 2022 IEEE International Carnahan Conference on Security Technology (ICCST), 2022, https://doi.org/10.1109/ICCST52959.2022.9896484
Articles in journals, other publications
  1. O. M. Gavrilik and A. V. Nazarenko, Phases of the Bose–Einstein Condensate Dark Matter Model with Both Two- and Three-Particle Interactions, Universe 2021, 7(10), 359. (Q2) https://doi.org/10.3390/universe7100359
  2. A.V. Zolotaryuk and Y. Zolotaryuk, Scattering data and bound states of a squeezed double-layer structure, J. Phys. A: Math. Theor. 54 (2021) 035201 (29pp) https://doi.org/10.1088/1751-8121/abd156
  3. O. Gamayun, N. Iorgov, Yu. Zhuravlev, Effective free-fermionic form factors and the XY spin chain, SciPost Phys. 10, 070 (2021). doi: DOI: 10.21468/SciPostPhys.10.3.070 [Not yet assigned quartile (2020). Impact Factor (2020): 6.16]
  4. T. Skrypnyk, N. Manojlovic "Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models", Nuclear Physics B, 967, 115424 (2021). Quartile 2020: Q1 https://doi.org/10.1016/j.nuclphysb.2021.115424
  5. T. Skrypnyk "Separation of Variables, Quasi-Trigonometric r-Matrices and Generalized Gaudin Models", SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 17, 069 (2021). Quartile 2020: Q2 https://doi.org/10.3842/SIGMA.2021.069
  6. T. Skrypnyk "On a class of gl (n)⊗ gl (n)-valued classical r-matrices and separation of variables", Journal of Mathematical Physics, 62, 063508, (2021). Quartile 2020: Q2 https://doi.org/10.1063/5.0041967
  7. T. Skrypnyk "Symmetric and asymmetric separation of variables for an integrable case of the complex Kirkhoff’s probleml", Journal of Geometry and Physics, 172,104418 (2022). Quartile 2020: Q2 https://doi.org/10.1016/j.geomphys.2021.104418
  8. Л. Ковальчук, Р. Олійников, Ю. Беспалов та ін.; за загальною редакцією Р. Олійникова, О. Кузнецова та О. Лемешка. Технології інформаційної безпеки в децентралізованих розподілених мережах. Частина 1. – Харків: Видавництво «Форт», 2021. – 300 с. ISBN 978-617-630-065-6
  9. Yuri Bespalov, Alberto Garoffolo, Lyudmila Kovalchuk, Hanna Nelasa, and Roman Oliynykov, Probability models of distributed proof generation for zk-SNARK-based blockchains, Mathematica 9 (2021), no. 23, 31pp, https://www.mdpi.com/2227-7390/9/23/3016 https://doi.org/10.3390/math9233016. Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics)
  10. Yuri Bespalov, Alberto Garoffolo, Lyudmila Kovalchuk, Hanna Nelasa, and Roman Oliynykov, Game-theoretic view on decentralized proof generation in zk-SNARK based sidechains, Cybersecurity Providing in Information and Telecommunication Systems (CPITS 2021), - CEUR Workshop Proceedings, vol. 2923, 2021, http://ceur-ws.org/Vol-2923/, pp. 47-59
Articles in journals, other publications
  1. A.M. Gavrilik, M.V. Khelashvili and A.V. Nazarenko. Bose-Einstein condensate dark matter model with three-particle interaction and two-phase structure, Phys. Rev. D 102 (2020), 083510 (13pp.).
  2. A. Zolotaryuk, Y. Zolotaryuk. Point interactions with bound states: A zero-thickness limit of a double-layer heterostructure, Low Temperature Physics (Fizika Nizkikh Temperatur), Vol. 46, 927–933 (2020).
  3. A.V. Zolotaryuk and Y. Zolotaryuk. Scattering data and bound states of a squeezed double-layer structure, Journ. of Physics A: Math. Theor. (2020), No.12, pp.1-34. DOI: 10.1088/1751-8121/abd156
  4. A.V. Nazarenko. Partition function of the Bose–Einstein condensate dark matter and the modified Gross–Pitaevskii equation, Int. J. Mod. Phys. D 29, No. 2 (2020) 2050018 (18 pages). DOI: 10.1142/S0218271820500182
  5. P. Gavrylenko, N. Iorgov, O. Lisovyy. Higher rank isomonodromic deformations and W-alge¬b¬ras, Lett. Math. Phys. 110, pp. 327–364 (2020), DOI: 10.1007/s11005-019-01207-6
  6. T. Skrypnyk. Separation of variables for quadratic algebras: algebras of Maillet and reflection-equation algebras, J. Math. Phys., Vol. 61, issue 8 (2020), paper id. 083504.
  7. G. Magnano, T. Skrypnyk. New separation of variables for the classical XXX and XXZ Heisenberg models, SIGMA, Vol. 16, 047, (2020)
  8. T. Skrypnyk. Symmetric separation of variables for trigonometric integrable models, Nuclear Physics B, 957, 115101, (2020).
  9. T. Skrypnyk. Separation of variables, Lax-integrable systems and gl(2)хgl(2)-valued classical r-matri¬ces, Journal of Geometry and Physics, 155, 103733, (2020).
  10. G. Bonelli, F. Del Monte, P. Gavrylenko, A. Tanzini. N = 2* Gauge Theory, Free Fermions on the Torus and Painlevé VI, Commun. Math. Phys. v. 377, pp. 1381–1419 (2020).
Preprints
  1. A.M. Gavrilik, M.V. Khelashvili and A.V. Nazarenko. Bose-Einstein condensate dark matter model with three-particle interaction and two-phase structure, arXiv: 2007.04832 [astro-ph.GA].
  2. A. Gamayun, N. Iorgov, Yu. Zhuravlev. Effective free-fermionic form factors and the XY spin chain, arxiv: 2012.02079.
  3. M. Lizunova, O. Gamayun. Solitary wave propagation in media with step-like inhomogeneuities, arXiv:2010.03385.
  4. A.V. Zolotaryuk and Y. Zolotaryuk. Scattering data and bound states of a squeezed double-layer structure, arxiv:2011.11437.
  5. O. Gamayun, A. Slobodeniuk, J.-S. Caux, O. Lychkovskiy. Nonequilibrium phase transition in transport through a driven quantum point contact, arXiv:2006.02400.
  6. Yu.Tykhyy. Finite orbits of monodromies of rank two Fuchsian systems, arXiv:2010.08477.
Papers at conferences and seminars
  1. Yu. Bespalov, L Kovalchuk, H. Nelasa, R. Oliynykov. On Generation of Cycles, Chains and Graphs of Pairing-Friendly Elliptic Curves, Proc. of IEEE International Scientific-Practical Conf. "Problems of Infocommunications. Science and Technology" (PIC S&T), Kharkiv 2020.
Articles in journals, other publications
  1. W.S. Chung, A.M. Gavrilik, A.V. Nazarenko, Photon gas at the Planck Scale within the doubly special relativity, Physica A: Stat. Mech. & Its Applics. 533 (2019), paper id.121928.
  2. A.M. Gavrilik, A.V. Nazarenko, Statistics effects in the extremal black holes ensemble, Int. J. Mod. Phys. A 34 (2019), paper id. 1950215 (16 pages).
  3. A.M. Gavrilik, I.I. Kachurik, M.V. Khelashvili, Galaxy rotation curves in the μ-deforma-tion-based approach to dark matter, Ukr. J. Phys. 64 (2019), No.11, pp. 1042-1049.
  4. A.M. Gavrilik, Yu.A. Mishchenko, Composite fermions as deformed oscillators: Wave-functions and entanglement, Ukr. J. Phys. 64 (2019), No.12, pp. 1034-1042.
  5. A.V. Zolotaryuk, G.P. Tsironis, Y. Zolotaryuk. Point interactions with bias potentials, Frontiers in Physics, 2019, vol. 7, No. 87.
  6. A.V. Zolotaryuk. Contact interactions in one-dimensional quantum mechanics: A family of generalized δ′-potentials, Ukr. J. Phys. 64 (2019), No. 11, pp. 1021-1028.
  7. P. Gavrylenko, N. Iorgov, O. Lisovyy, Higher rank isomonodromic deformations and W-algebras, Lett. Math. Phys. (2019), Online: 14 September 2019, pp. 1-38, https://doi.org/10.1007/s11005-019-01207-6
  8. Yu. Bespalov, Categories: Between Cubes and Globes. Sketch I, Ukr. J. Phys. 64 (2019), No. 12, pp. 1125-1128.
  9. Skrypnyk T. Classical r-matrices elliptic BCS and Gaudin models and spectral problem, Nuclear Physics B, 941, 225-248 (2019).
  10. Skrypnyk T. Symmetric separation of variables in the Clebsch system, Journal of Geometry & Physics, 135 (2019), pp.204-218.
  11. Skrypnyk T., Dubrovin B. Separation of variables for quadratic Lax algebras and skewsymmetric classical r-matrices, Journ.f Math. Phys., 60 (2019), 093506.
  12. M. Cafasso, P. Gavrylenko, O. Lisovyy, Tau functions as Widom constants, Commun. Math. Phys. 365 (2019), p. 741.
  13. M. Bershtein, P. Gavrylenko, A. Marshakov, Cluster Toda chains and Nekrasov functions, Theor. Math. Phys. 198 (2019), p. 157.
  14. P. Gavrylenko, R. Santachiara, Crossing invariant correlation functions at c=1 from isomonodromic τ functions, J. High Energy Phys. (2019) 2019: 119.
Preprints
  1. A.V. Nazarenko, Partition function of the Bose–Einstein condensate dark matter and the modified Gross–Pitaevskii equation, arXiv:1910.00232 [astro-ph.GA].
  2. G. Bonelli, F. Del Monte, P. Gavrylenko, A. Tanzini, N=2∗ gauge theory, free fermions on the torus and Painlevé VI, arXiv:1901.10497 [hep-th].
  3. G. Bonelli, F. Del Monte, P. Gavrylenko, A. Tanzini, Circular quiver gauge theories, isomonodromic deformations and WN fermions on the torus, arXiv:1909.07990 [hep-th]
Papers at conferences and seminars
  1. A.M. Gavrilik, I.I. Kachurik, Hamiltonians built from pseudo-Hermitian position/ momen-tum operators, and nonlinear Bogolyubov transformations, XI Bolyai-Gauss-Lobachevsky (BGL-2019) International Conference: Non-Euclidean, Non-Commutative Geometry and Quan¬tum Physics, May 19 - 24, 2019, Kiev, Ukraine. Book of Abstracts, p.12.
  2. Khelashvili M.V., Gavrilik A.M., Kachurik I.I. Galaxy rotation curves in the μ-deformation based approach. XI Bolyai-Gauss-Lobachevsky (BGL-2019) International Conference: Non-Euclidean, Non-Commutative Geometry and Quantum Physics, May 19 - 24, 2019, Kiev, Ukraine. Book of Abstracts, p.19.
  3. A.V. Nazarenko, A.M. Gavrilik, Statistics effects in extremal black hole ensemble, XI Bolyai-Gauss-Loba¬chevsky (BGL-2019) International Conference: Non-Euclidean, Non-Com¬mu¬tative Geometry and Quantum Physics, May 19-24, 2019, Kiev, Ukraine. Book of Abstracts, p.29.
  4. A.M. Gavrilik, I.I.Kachurik, New deformed Heisenberg algebra from the μ-deformation based model of dark matter, Bogolyubov Kyiv Conference Problems of Theoretical and Mathematical Physics, Sept. 24 – 26, 2019, Program and Abstracts, p. 28.
  5. Yu.A. Mishchenko, A.M. Gavrilik, Concept of Duality of deformed analogs of Bose gas model, and its applications, Bogolyubov Kyiv Conference Problems of Theoretical and Mathematical Physics, Sept. 24 – 26, 2019, Program and Abstracts, p. 76.
  6. Yu.A. Mishchenko, A.M. Gavrilik, Composite quantum particles as deformed oscillators oscillators: wave¬function, entanglement and implications , XI Bolyai-Gauss-Lobachevsky (BGL-2019) International Conference: Non-Euclidean, Non-Commutative Geometry and Quantum Physics, May 19-24, 2019, Kiev, Ukraine. Book of Abstracts, p.27.
  7. A.V. Zolotaryuk. Contact interactions in quantum mechanics, XI Bolyai-Gauss-Lobachevsky (BGL-2019) International Conference: Non-Euclidean, Non-Commutative Geometry and Quant.Physics, May 19-24, 2019, Kiev, Ukraine. Book of Abstracts, p. 47.
  8. A.V. Zolotaryuk. Contact interactions in heterostructures: A squeezed limit, International Conference CHAOS 2019, 12th Chaotic Modeling and Simulation, Book of Abstracts, p. 139.
  9. M. Khelashvili, A. Gavrilik, I. Kachurik, Modeling of galaxy rotation curves using nonstandard (µ-deformed) statistics. Intt. School of Subnucl. Phys., 57th Course: In search for the unexpected (ISSP 2019) 21-30 June 2019, EMFCSC, Erice, Italy.
  10. M. Khelashvili, A. Gavrilik, I. Kachurik, Galaxy Rotation Curves Within µ-Deformed Dark Matter Model 28th Annual Student Conference: Week of Doctoral Students 2019, 4-6 June 2019, Charles University, Prague, Czech Republic. WDS'19 Proceedings of Contributed Papers: Part III — Physics, Prague, Matfyzpress, pp. 48-49, 2019.
  11. Yu. Bespalov Categories: between cubes and globes., XI Bolyai-Gauss-Lobachevsky (BGL-2019) International Conference: Non-Euclidean, Non-Commutative Geometry and Quantum Physics, May 19-24, 2019, Kiev, Ukraine. Book of Abstracts, p. 7.
Articles in journals, other publications
  1. A.M. Gavrilik, I.I. Kacurik, M.V. Khelashvili, A.V. Nazarenko. Condensate of μ-Bose gas as a model of dark matter, Physica A: Stat. Mech. & Its Applics. 506 (2018), pp.835-843.
  2. A.M. Gavrilik. Geometric Aspects and Some Uses of Deformed Mo¬dels of Thermostatistics, Universe, vol. 4 (2018), paper id. 0033, 11 pages.
  3. A.M.Gavrilik, I.I.Kachurik. Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscilators, Mod. Phys. Lett. A (December 2018), online DOI:https://doi.org/10.1142/S021773231950007X
  4. A.V. Zolotaryuk. Origin of resonant tunneling through single-point barriers, Physica E: Low-dimens. Systems & Nanostruct. 103 (2018), pp. 81-86.
  5. A.V. Zolotaryuk. A phenomenon of splitting resonant-tunneling one-point interactions, Annals of Physics, 2018, vol. 396, pp. 479-494.
  6. P. Gavrylenko, N. Iorgov, O. Lisovy. On solutions of the Fuji-Suzuki-Tsuda system, SIGMA 14 (2018), paper. id. 123, 27 pages.
  7. T. Skrypnyk. Modified n-level, n-1 mode Tavis-Cummings model and algebraic Bethe ansatz, J. Phys. A: Math. Theor. 51 (2018), paper id. 015204, 12 pages.
  8. T. Skrypnyk. Reductions in soliton hierarchies and special points of classical r-matrices, J. Geom. & Phys. 130 (2018), pp.260-287.
  9. T. Skrypnyk. Separation of variables in the anisotropic Shottky-Frahm model, Theor. Math. Phys. 196 (2018), pp.1359-1377.
  10. T. Skrypnyk. B. Dubrovin, Separation of variables for linear Lax algebras and classical r-matrices, J. Math. Phys. 59 (2018), paper. id. 091405, 18 pages.
  11. A.M. Pavlyuk. Generalized Equidistant Chebyshev Polynomials and Alexander Knot Invariants, Ukr. J. Phys. 63 (2018), No. 6, pp. 488-494.
  12. C. Marboe, D. Volin. The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system, J. Phys. A 51 (2018), paper id. 165401, 53 pages.
Articles in journals, other publications
  1. A.V. Zolotaryuk. Families of one-point interactions resulting from the squeezing limit of the sum of two- and three-delta-like potentials. J. Phys. A: Math. Theor., 2017, 50, 225303 (19pp).
  2. A.V. Nazarenko, V. Blavatska. A one-dimensional random walk in a multi-zone environment, J. Phys. A: Math. Theor., 50, 185002 (2017), 11 pp.;
  3. A.V. Nazarenko, V. Blavatska. Asymmetric random walk in a one-dimensional multizone environment, Ukr. J. Phys., 62, № 6 (2017), pp. 508-517;
  4. T. Skrypnyk. Separation of variables in anisotropic models and non-skew-symmetric elliptic r-matrices, Letters in Mathematical Physics, V. 107, No 5, (2017), p.793-812.
  5. T. Skrypnyk. Separation of variables in anisotropic models: anisotropic Rabi and elliptic Gaudin model in an external magnetic field, J. Phys. A: Math. Theor., 50, 325206 (2017).
  6. M.A. Bershtein, A.I. Shchechkin. Backlund transformation of Painleve III (D8) tau function, J. Phys. A: Math. Theor. 50 (2017) 115205, 28 pages.
  7. M.A. Bershtein, A.I. Shchechkin. q-deformed Painleve tau function and q-deformed conformal blocks, J. Phys. A: Math. Theor. 50 (2017) 085202, 21 pages.
  8. Christian Marboe, Dmytro Volin. Fast analytic solver of rational Bethe equations, J. Phys. A: Math. Theor., 50 (2017), 204002, 12 pages.
Articles in journals, other publications
  1. Gavrilik A.M., Kachurik I.I., New version of pseudo-Hermiticity in the Two-Sided Defor­mation of Heisenberg Algebra, Mod. Phys. Lett. A 31, no.4 (2016) paper 1650024 (14 pp.).
  2. Alexandre M. Gavrilik, Ivan I. Kachurik, Nonstandard Deformed Oscillators from q- and p, q-Deformations of Heisenberg Algebra, SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), 12 (2016) paper 047 (12 pp.).
  3. Nazarenko A.V., Kulinich Yu.A. Relativistic kinematics of two-parametric Riemann surface in genus two. Hadronic J. 39, 181-198 (2016).
  4. О.В. Золотарюк, Л.С. Брижик, Я.О. Золотарюк, Солітонна динаміка в м'яких молекулярних структурах, В книзі Наукова рада з проблеми Фізика м'якої речовини (Львів-Київ, 2016) с. 34-43.
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