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Information × Registration Number 0217U001556, 0112U000052 , R & D reports Title Nonlinear quantum oscillators, integrable models and quantum field systems: symmetries and applications popup.stage_title Head Gavrilik Alexandre Mykhailovych, Registration Date 28-02-2017 Organization Bogolyubov Institute for Theoretical Physics of National Academy of Sciences of Ukraine popup.description2 The report bases on the results of 102 scientific papers, among which 59 papers, done in the department during 2012–2016yy and published in major ukrainian and international profile journals. Investigations within this project vere devoted to several important problems in the theory of deformed (nonlinear) quantum oscillators and their applications,algebraic, topological and categorical aspects of quantum integrable systems, quantum statistical and quantum-field theories. New deformed extensions are constructed for ther Heisenberg algebra as well as nonstandard algebras/models of deformed quantum oscillatorsз with one or more deformation parameters and their main properties studied - infinite dimensional representations, spectra of thge Hamiltonian and degeneracy of energy levels, pseudo-hermiticity of observables operators, coherent states, etc. Physics applications are given, among which diverse deformations of the Bose gas along with their thermostatistical aspects, and also to the construction of the new 5-parametric extensions of the Virasoro algebra and related versions of 2-dimensional conformal field theory. Realizations of the algebras of operators of composite bosons/composite fermions in terms of algebras of deformed oscillators of Bose- or Fermi-type. For such composite particles, a link is uncovered between their entangled states and the very entanglement - basic concepts in quantum information theory – and the respective deformed oscillators and the deformation parameter. New physically motivated one and two-parametric deformed analogs of Bose gas model aredeveloped aimed at the effective description of the inter-particle interactions jointly with their compositeness. For these models, main thermodynamical functions and higher order distribution functions are derived, along with correlation functions. The connection is found between quantum field theory with conformal symmetry and the theory of isomonodromic deformations of the Fuks matrix differential equations. This onnection has enabled to find explicit expansion fot the two-point correlation function in the sine-Gordon model at the free fermion point. Integrable spin model of Godain type and diverse extensions of the Janes-Cummings Dikke are obtained. These extensions are based on the developed theory of non-skew-symmetric classical r-matrices. Product Description popup.authors Іоргов Микола Зіновійович Безвершенко Юлія Василівна Беспалов Юрій Миколайович Бурбан Іван Макарович Гаврилик Олександр Михайлович Кучерявий Валентин Іванович Міщенко Юрій Анатолійович Мороз Олег Миколайович Назаренко Андрій Володимирович Павлюк Анатолій Миколайович Ребеш Анастасія Петрівна Скрипник Тарас Володимирович Тихий Юрій Володимирович popup.nrat_date 2020-04-02 Close