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List of Departments Topmost Scientific Publications
🗀 Archive 2010-2015
Department of Mathematical Methods in Theoretical Physics
Articles in journals, other publications
  1. A.M. Gavrilik, Yu.A. Mishchenko. Correlation function intercepts for μ̃, q-deformed Bose gas model implying effective accounting for interaction and compositeness of particles, Nucl. Phys. B, Vol. 891 (2015), 466-481.
  2. N. Iorgov, O. Lisovyy, J. Teschner. Isomonodromic Tau-Functions from Liouville Conformal Blocks, Commun. Math. Phys., Vol. 336, Issue 2 (2015), pp. 671-694.
  3. O. Gamayun, Yu. V. Bezvershenko, V. Cheianov. The fate of a gray soliton in a quenched Bose-Einstein condensate. Phys. Rev. A. Vol. 91 (2015), paper 031605.
  4. T. Skrypnyk. General integrable n-level many-mode Jaynes-Cummings-Dicke models and classical r-matrices with spectral parameters, J. Math. Phys. Vol. 56 (2015), paper 023511.
  5. T. Skrypnyk. Gaudin-type models, non-skew-symmetric classical r-matrices and nested Bethe ansatz, Nucl. Phys. B. 891 (2015), p. 200-229.
  6. T. Skrypnyk. Quantum integrable models of interacting bosons and classical r-matrices with spectral parameters J. Geom. Phys. v.97 (2015), pp. 133-155.
  7. P. Gavrylenko. Isomonodromic τ-functions and W N conformal blocks, Journal of High Energy Physics, 2015:167 (Online: 24 Sept. 2015).
  8. M.A. Bershtein, A.I. Shchechkin. Bilinear Equations on Painlevé τ Functions from CFT, Commun. Math. Phys. V.339 (2015), Issue 3, pp.1021-1061.
Articles in journals, other publications
  1. A.M. Gavrilik, Yu.A. Mishchenko. Virial coefficients in (μ,q)-Bose gas model related to com-positeness of particles and their interaction: Temperature-dependence problem, Phys. Rev. E vol. 90, 2014, 52147 (8pp.).
  2. N. Iorgov, O. Lisovyy, J. Teschner. Isomonodromic Tau-Functions from Liouville Confo-rmal Blocks, Commun. in Mathem. Physics, 2014, vol. 333, Issue 1; DOI: 10.1007/s00220-014-2245-0.
  3. N. Iorgov, O.Lisovyy, A.Shchechkin, Yu. Tykhyy. Painleve Functions and Conformal Blocks, Constructive Approximation, 2014, vol. 39, Issue 1, pp. 255-272.
  4. A. Its, O. Lisovyy, Yu. Tykhyy. Connection Problem for the Sine-Gordon/Painleve III Tau Function and Irregular Conformal Blocks, Internat. Math. Research Notices, Nov. 2014, doi:10.1093/imrn/rnu209.
  5. O. Lisovyy, Yu. Tykhyy. Algebraic solutions of the sixth Painleve equation, Journal of Geometry and Physics, vol. 85, Nov. 2014, pp. 124-163.
  6. T. Skrypnyk. Decompositions of quasigraded Lie algebras, non-skew-symmetric classical r-matrices and generalized Gaudin models, J. Geom. Phys. 2014, vol. 75, 98-112 .
  7. T. Skrypnyk. Generalized shift elements and classical r-matrices: construction and applications, J. Geom. Phys. 2014, vol. 80, 71-87 .
  8. T. Skrypnyk. Many-poled r-matrix Lie algebras, Lax operators, and integrable systems, J. Math. Phys., 2014, vol. 55, 083507.
  9. A.M. Pavlyuk. Polynomial invariants of torus knots and (p, q)-calculus, Algebras, Groups and Geometries, vol. 31, No.2, (2014) 175-182.
  10. O. Moroz. Analytical formulas for shear and bulk viscosities in relativistic gaseous mix-tures with constant cross sections, Computers & Fluids, 2014, vol. 90, p. 9.
Articles in journals, other publications
  1. A.M. Gavrilik, Yu.A. Mishchenko. Energy dependence of the entanglement entropy of composite boson (quasiboson) systems, J.Phys. A: Math. Theor. 46 (2013) 145301 (20pp).
  2. І.M. Burban. Unified (p, q;α, γ, l)-deformation of oscillator algebra and two-dimensional conformal field theory, Phys. Lett. A 377, 2863 (2013).
  3. O. Gamayun, N. Iorgov, O. Lisovyy. How instanton combinatorics solves Painlevé VI, V and III's, J. Phys. A: Math. Theor. 46 (2013) 335203
  4. N. Iorgov, A.I. Molev, E. Ragoucy. Casimir elements from the Brauer-Schur-Weyl duality, J. of Algebra 387 (2013), 144-159.
  5. N. Iorgov, O. Lisovyy, Yu. Tykhyy. Painleve VI connection problem c=1 conformal blocks, J. High Energy Phys. 12 (2013) paper 029 (25pp.).
  6. T. Skrypnyk. The N-level, N-1 mode Jaynes-Cummings model: spectrum and eigenvalues, J. Phys. A: Math. Theor. 46 (2013) 052001 (18pp.).
  7. T. Skrypnyk. Z2-graded Gaudin models and analytical Bethe ansatz, Nucl. Phys. B 879, p.495 (2013).
  8. T. Skrypnyk., Infinite-dimensional Lie algebras, classical r-matrices and Lax operators: two approaches, J. Math. Phys., v.54 (2013), paper 103507.
  9. A.M. Gavrilik, I.I. Kachurik, A.V. Lukash. New version of q-deformed supersymmetric quantum mechanics, Ukr. J. Phys. V.58, no.11, pp.1025-1032 (2013).
  10. A.M. Gavrilik, Yu.A. Mishchenko. Deformed Bose gas models aimed at taking into account both compositeness of particles and their interaction, Ukr. J. Phys. 58, N.12, p.1171-1177 (2013).
  11. A.P. Rebesh, I.I. Kachurik, A.M. Gavrilik. Elements of µ-calculus and thermodynamics of µ- Bose-gas model, Ukr. J. Phys. V.58, no. 12, pp. 1182-1191 (2013).
  12. I.M. Burban. Unified (p, q;α, β, l)-deformations of oscillator, hybrid oscillator algebras and two- dimensional conformal field theory, Ukr. J. Phys. v.58, N 11 (2013), pp. 1114-1124.
  13. A.V. Nazarenko. Area quantization of the parameter space of Riemann surfaces in genus two, Ukr. J. Phys. v.58, № 11 (2013), 1055-1064.
  14. Yu. Bespalov. From bialgebras to operads. Quantum line and cooperad of correlation functions, Ukr. J. Phys. v.58, № 11 (2013), 1033-1045.
  15. Pavlyuk A.M. Generalization of polynomial invariants and holographic principle for knots and links, Ukr. J. Phys. v.58, N 7 (2013), pp. 673-676.
  16. A.M. Pavlyuk. HOMFLY polynomial invariants of torus knots and bosonic (q, p)-calculus, Ukr. J. Phys. v.58, N 12 (2013), pp. 1178-1181.
  17. Yu. Bezvershenko, P.I. Holod. Extended State Space of the Rational sl(2) Gaudin Model in Terms of Laguerre Polynomials, Ukr. J. Phys. v.58, N.11 (2013), p.1084-1091.
  18. A.V. Kozak. Integrability in AdS/CFT, Ukr. J. Phys. v.58, N 11 (2013), p.1108-1112.
  19. O.V. Moroz. Shear and Bulk Viscosities of a Hadron Gas within Relaxation Time Approxi- mation and Its Test, Ukr. J. Phys. v.58, N 12 (2013), 1127-1131.
Articles in journals, other publications
  1. A.M. Gavrilik, A.P. Rebesh, Deformed gas of p, q-bosons: virial expansion and virial coefficients, Mod. Phys. Lett. B 26, No.5 (2012) 1150030 (13 pp).
  2. A.M. Gavrilik, Yu.A. Mishchenko, Entanglement in composite bosons realized by deformed oscillators, Phys. Lett. A 376, No. 19 (2012), pp.1596-1600.
  3. A.M. Gavrilik, Yu.A. Mishchenko, Exact expressions for the intercepts of r-particle momentum correlation functions in μ-Bose gas, Phys. Lett. A 376, No.36 (2012), 2484-2489
  4. A.M. Gavrilik, I.I. Kachurik, Three-parameter (two-sided) deformation of Heisenberg algebra, Mod. Phys. Lett. A 27, No. 21 (2012) 1250114, arXiv:1204.2817.
  5. P. Gavrylenko, N. Iorgov, O. Lisovyy, Form factors of twist fields in the lattice Dirac theory, J. Phys. A: Math. Theor. 45 (2012) 025402.
  6. O. Gamayun, N. Iorgov, O. Lisovyy, Conformal field theory of Painleve VI, J. of High Energy Phys., Vol. 2012, No. 10 (2012), 38.
  7. T. Skrypnyk, Quasi-periodic functions on the torus and sl(n)-elliptic Lie algebra. J.Math. Phys. 53 (2012), 023502-023521.
  8. T. Skrypnyk, Quasigraded bases in loop algebras and classical rational r-matrices. J.Math. Phys. 53 (2012), 083501-083520.
  9. T. Skrypnyk, Rational r-matrices, higher rank Lie algebras and integrable proton- neutron BCS models. Nuclear Physics B 863, Issue 2 (2012), 435-469.
  10. T. Skrypnyk, Non-skew-symmetric classical r-matrices and integrable px+ipyproton- neutron BCS models, Nuclear Physics B 864, Issue 3 (2012) 770-805.
  11. T. Skrypnyk, Classical r-matrices and integrable BCS models with many types of fermions. J. Phys. A: Math. Theor. 45 (2012) 415203-415224.
  12. T. Skrypnyk, Elliptic three-boson system. two-level three-modeJCD-type models and nonskew-symmetric classical r-matrices.Nuclear Physics B 856, Issue 3 (2012), 552-576.
  13. B. Dubrovin, T. Skrypnyk, Classical double, R-operators, and negative flows of integrable hierarchies. Theor. Math. Phys. 172 (2012), 911-931.
  14. I.M. Burban, Generalized deformed oscillators in the framework of unified (q;α, β, γ, ν)- deformation and their oscillator algebras, Ukr. J. Phys., v.57, № 4 (2012), p. 396-407.
  15. A.M. Pavlyuk, On T(n, 4) torus knots and Chebyshev polynomials, Ukr. J. Phys. v.57, № 4, (2012), p.439-442.
Articles in journals, other publications
  1. A.M. Gavrilik, I.I. Kachurik, Yu.A. Mishchenko, Two-fermion composite quasi-bosons and deformed oscillators, Ukr. J. Phys. v. 56, No.9, 948-954 (2011).
  2. A.M. Gavrilik, A.M. Pavlyuk, Alexander Polynomial Invariants of Torus Knots T(n, 3) and Chebyshev Polynomials, Ukr. J. Phys. v. 56, No.7, 680-687 (2011).
  3. I.M. Бурбан, Новій фізиці нову математику і концептуальна інтерпретація R-операції Боголюбова-Парасюка, в пам'ятній збірці. ОСТАП ПАРАСЮК. Слава української науки(укладачі Н.Вірченко, В. Козирський), Київ, 2011, c.309-353.
  4. В.I. Кучерявий, R-операція Боголюбова-Парасюка: джерела, суть, потенціал, здобутки, подальший розвиток, в пам'ятній збірці. ОСТАП ПАРАСЮК. Слава української науки(укладачі Н.Вірченко, В. Козирський), Київ, 2011, c.354-361.
  5. A.M. Gavrilik, A.P. Rebesh, Intercepts of the momentum correlation functions in ?-Bose gas model and their asymptotics, Europ. Phys. J. A 47, paper 55 (2011), pp.1-8.
  6. A.M. Gavrilik, I.I. Kachurik, Yu.A. Mishchenko, Quasibosons composed of two q-fermions: realization by deformed oscillators, J.Phys.A: Math.Theor. 44, paper 475303 (2011), p.-23.
  7. N. Iorgov, V. Shadura, Yu. Tykhyy. Spin operator matrix elements in the quantum Ising chain: fermion approach. J. Stat. Mech., 1102, P02028 (2011), pp.1-19.
  8. N. Iorgov, O.Lisovyy, Ising correlations and elliptic determinants, J.Stat.Phys.143(2011), 33-59
  9. N. Iorgov, O. Lisovyy, Finite-lattice form factors in free-fermion models, J. Stat. Mech., 1104, P04011 (2011), pp.1-12.
  10. N. Iorgov, Form factors of the finite quantum XY-chain, J. Phys. A: Math. Theor. 44, Issue 33, paper 335005 (2011), pp.1-20.
  11. A.V. Nazarenko. Directed random walk on the lattices of genus two, Int. J. Mod. Phys. B, 25, No.26 (2011), pp.3415-3433.
  12. Yu. Bezvershenko, P. Holod. Dynamical stabilization of spin systems in time-dependent magnetic fields. Physica Scripta T143 (2011), paper 014005 (5pp).
  13. Yu.V. Bezvershenko, P.I. Holod, Resonance in a driven two-level system: analytical results without the rotating wave approximation, Physics Letters A, 375 (2011), pp.3936-3940.
  14. T. Skrypnyk . General integrable two-level, one-mode Jaynes-Cummings-Dicke models and classical r-matrices with spectral parameters, J. Stat. Mech. (2011) P10009. 18 pp.
  15. Nikolay Gromov, Didina Serban, Igor Shenderovich, Dmytro Volin, Quantum folded string and integrability: from finite size effects to Konishi dimension, JHEP 1108: 046, 2011
Articles in journals, other publications
  1. A.M. Gavrilik, A.M. Pavlyuk, On Chebyshev polynomials and torus knots, Ukr. J. Phys. v. 55, N 1, 129-134 (2010).
  2. N.Z. Iorgov, Spontaneous Magnetization of Quantum XY-chain from Finite Chain Form-factors, Ukr. J. Phys. v. 55, N 1, 116-120 (2010).
  3. A.V. Nazarenko, Glasma evolution in partonic medium, J. Phys. Stud., v. 14, N 3, 3202 (2010).
  4. V.I. Kucheryav, Self-consistent renormalization as an efficient realization of main ideas of the Bogoliubov-Parasiuk R-operation, Ukr. J. Phys. v.55, N 5, p.487-504 (2010).
  5. S.V. Kutnii, P.I. Holod, Four-fermion Interaction in the Low-energy Approximation of Quantum Chromodynamics, Ukr. J. Phys. v. 55, N 11, p.1161-1164 (2010).
  6. Ю.В. Тихий, Власні стани скінченних вантових інтегровних систем. Авторефереат на здобуття наукового кандидата фізико-математичних наук. Київ - 2010. 16 с.
  7. A.M. Gavrilik, A.P. Rebesh, Polynomially deformed oscillators as k-bonacci oscillators, J. Phys. A:Math. Theor. 43 095203 (15pp) (2010).
  8. A.M. Gavrilik, I.I. Kachurik, A.P. Rebesh, Quasi-Fibonacci oscillators, J. Phys. A: Math. Theor. v. 43 245204 (16pp) (2010).
  9. I. M. Burban, Generalized deformed harmonic oscillator in framework of unified (q;α, β, γ, ν)-deformation, Mod. Phys. Lett. A, 25 1239 (2010).
  10. I. M. Burban, Arik-Coon oscillator with q>1 in framework of united (q;α, β, γ, ν)-deformation, J. Phys. A:Math. Theor., 43 3052 04 (2010) .
  11. N. Iorgov, S. Pakuliak, V. Shadura, Y. Tykhyy, G. von Gehlen. Spin operator matrix elements in the superintegrable chiral Potts quantum chain, J. Stat. Phys., V 139, no. 5, pp.743-768 (2010).
  12. T. Skrypnyk, Isomonodromic deformations, generalized Knizhnik-Zamolodchikov equations and non-skew-symmetric classical r-matrices, J. Math. Phys., V 51, no.8, p.3516-24 (2010).
  13. T. Skrypnyk, Generalized Knizhnik-Zamolodchikov equations, off-shell Bethe ansatz and non-skew-symmetric classical r-matrices, Nucl. Phys. B, V 824, no. 3, p. 436 (2010).
  14. T. Skrypnyk, Generalized Gaudin systems in an external magnetic field and reflection equation algebras, J. Stat Mech.: Theor. Exp., no.6, p.06028 (2010).
  15. T. Skrypnyk, Lie algebras with triangular decompositions, non-skew-symmetric classical r-matrices and Gaudin-type integrable systems, J. Geom. Phys., V 60, no. 3, p. 491 (2010).
  16. T. Skrypnyk, Integrable modifications of Dicke and Jaynes-Cummings models, Bose-Hubbard dimers and classical r-matrices, J. Phys. A: Math. Theor., V 43, no. 20, p. 205205 (2010).
Preprints
  1. N. Iorgov, V. Shadura, Yu. Tykhyy. Spin operator matrix elements in the quantum Ising chain: fermion approach. arXiv:1011.2603.
  2. B. Dubrovin, T. Skrypnyk, Classical double, R-operators and negative flows of integrable hierarchies. arXiv:1011.4894.
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