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Information × Registration Number 0223U000836, 0122U001575 , R & D reports Title Magnetic properties of mesoscopic systems with internal degrees of freedom popup.stage_title Head Ratkevych Serhii S., Кандидат фізико-математичних наук Registration Date 20-01-2023 Organization V.N. Karazin Kharkiv National University popup.description2  Magnetic systems composed of a finite number of interacting atoms in degenerate multiparticle quantum states of ideal gases subject to Bose-Einstein or Fermi-Dirac statistics, captured in harmonic potentials of optical traps for neutral atoms are the object of the research work. The purpose of the work is to identify the manifestations of a finite number of atoms in the thermodynamic characteristics of gases, to improve the accuracy of theoretical analysis using modern numerical algorithms of molecular dynamics, and to accurately diagonalize Hamiltonians. The limits of applicability of the semi-classical approach is considered. For this purpose, precise temperature dependences of chemical potentials in systems consisting of a finite number of trapped atoms are constructed. For a gas with Fermi statistics, the deviations in the Fermi energy values originating from the discrete structure of the spectrum are demonstrated. It is shown that they appear only for a small number of particles. A characteristic softening of the features of the phase transition is observed for the Bose gas, which contrasts with semiclassical predictions and similar approximations. The accurate methodology for determining the corrections to the critical temperature due to the finite number of atoms is proposed. At the same time, it is noted that the concept of phase transition in these systems is not correct in the strict sense due to the smooth nature of all thermodynamic functions. The obtained results are valuable from the point of view of theoretical approaches and experiments aimed at the exact determination of the transition temperature change in weakly interacting Bose gases. By improving the description of systems with a finite number of particles, it is possible to make more accurate predictions about the influence of interaction effects in systems with cold atoms. This is relevant in view of the latest developments in theoretical and experimental approaches in this field. Product Description popup.authors Bohatyrenko Serhii I. Hirka Ihor O. Naumovets Artem S. Slyusarenko Yuriy Victorovich Sotnikov Andriy G. popup.nrat_date 2023-01-20 Close