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Information × Registration Number 0219U100679, 0117U003534 , R & D reports Title Description of quantum gases with interaction, and of entanglement aspects, based on deformed algebras and kinetic methods popup.stage_title Head Mishchenko Yurii A., Кандидат фізико-математичних наук Registration Date 25-02-2019 Organization Bogolybov Institute for Theoretical Physics of NASU popup.description2 Object of study: quantum gases with interaction, or in a trap; galactic-halos dark matter. Goal of work: study of quantum gases with interaction at microscopic level, and elaboration of their effective description based on deformed algebras (DAs). Application of DAs, and of thermodynamic geometry method, to the description of dark matter properties. Research methods: quantum statistical physics, application of DAs, thermodynamic geometry. Task on taking interaction into account is divided into 2 stages: I. gas in trap; II. account for particles interaction. Results are original. On stage I, we treat Bose gas in isotropic trap U(r)= A r^n + B r^(-m), in D dimensions, and find total number of particles. Within effective account for particles interaction, operators' DAs, and their boson expansions are used. Secondary quantized relations, on DAs operators, written. Meaning of the result – initial system with interaction is reduced to en effective model of noniteracting, but deformed bosons. Introduced is the concept of "duality" of deformed Bose gas models (DBGMs) – i.e. of a kind of equivalence between DBGMs of two types: (a) defined thru deformed derivative, like Jackson one, with respect to fugacity z, or (b) constructed in terms of deformed oscillator algebra. We apply relation of "duality" to gases with interaction, and obtain interesting physical implications. The model of dark matter, consisting of condensate of deformed μ-Bose gas, is proposed. Within approach of Ruppeiner geometry, possibility of phase transition in the system is proved. Main parameters of the dark matter halo are found. The model of (μ̃,µ)-Bose gas is developed, thermodynamics of this gas is built, main thermodynamic quantities and relations found. Based on Ruppeiner geometry, possibility of phase transition in this gas is examined. Keywords: inter-particle interaction, deformed oscillators, Bose condensation, q-, µ-Bose gas, dark matter, Ruppeiner thermodynamic geometry. Product Description popup.authors Mishchenko Yurii A. Khelashvili Mariia V. popup.nrat_date 2020-04-02 Close