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Information × Registration Number 0223U000930, 0120U102252 , R & D reports Title The influence of internal degrees of freedom of particles on the physical characteristics of quantum systems near phase transitions. popup.stage_title Head Girka Igor O., Доктор фізико-математичних наук Registration Date 22-01-2023 Organization V.N. Karazin Kharkiv National University popup.description2  The object of the study was a system of many interacting particles of spin-1 in the context of homogeneous ultracold gases. The objective of the study was to construct the general Hamiltonian of such a system taking into account both the spin and quadrupole degrees of freedom under the pairwise interparticle interaction and the assumption of their inequality, the study of the role of nonlocality of such an interaction, as well as the further application of the derived Hamiltonian to study the magnetic properties of the Bose-Einstein condensate of atoms with a spin-1 in the magnetic field. The Hamiltonian of the system of many particles with spin-1 interacting pairwise has been obtained and substantiated. This Hamiltonian contains eight generators of the SU(3) group, among which three are spin components and the remaining five are associated with quadrupole degrees of freedom. In particular, the unequal contribution from spin and quadrupole exchange interactions is taken into account. It is shown that such a Hamiltonian is valid only for the potential of a nonlocal interaction, while for a local interaction given by the s-scattering length, the Hamiltonian should be bilinear in spin operators (that is, it will be of the Heisenberg type). The obtained Hamiltonian was applied to obtain the basic equation describing the magnetic properties of the Bose-Einstein condensate of atoms with a spin-1 in a magnetic field. Analytical solutions of this equation were found and it was shown that the Bose-Einstein condensate can be in ferromagnetic, quadrupolar, or paramagnetic states. Expressions for the corresponding magnetizations were also obtained. These equations also make it possible to further analyze the thermodynamic characteristics of the specified magnetic states and spectra of single-particle excitations. The acquired new knowledge is of interest as a scientific basis for the design and manufacture of devices for storage, encryption and transmission of quantum informat Product Description popup.authors Girnyk Serhii A. Lazuryk Valentyna Mykhaylivna Sliusarenko Yurii V. Sotnikov Andriy G. Yunakova Olga M. popup.nrat_date 2023-01-22 Close