Thermodynamic characteristics of ideal quantum gases in harmonic potentials within exact and semiclassical approaches

Valeriia Bilokon, Elvira Bilokon, Alexander Peletminskii and Andrii Sotnikov

Physica A: Statistical Mechanics and its Applications, 2022, vol. 589, issue C

Abstract: We theoretically examine equilibrium properties of the harmonically trapped ideal Bose and Fermi gases in the quantum degeneracy regime. We analyze thermodynamic characteristics of gases with a finite number of atoms by means of the known semiclassical approach and perform comparison with exact numerical results. For a Fermi gas, we demonstrate deviations in the Fermi energy values originating from a discrete level structure and show that these are observable only for a small number of particles. For a Bose gas, we observe characteristic softening of phase transition features, which contrasts to the semiclassical predictions and related approximations. We provide a more accurate methodology of determining corrections to the critical temperature due to finite number of particles.

Keywords: Bose gas; Fermi gas; Harmonic trap; Phase transition; Semiclassical approach; Finite number of particles (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:589:y:2022:i:c:s0378437121008682

DOI: 10.1016/j.physa.2021.126605

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