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

Author

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  • Bilokon, Valeriia
  • Bilokon, Elvira
  • Peletminskii, Alexander
  • Sotnikov, Andrii

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.

Suggested Citation

  • Bilokon, Valeriia & Bilokon, Elvira & Peletminskii, Alexander & Sotnikov, Andrii, 2022. "Thermodynamic characteristics of ideal quantum gases in harmonic potentials within exact and semiclassical approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    • Handle: RePEc:eee:phsmap:v:589:y:2022:i:c:s0378437121008682
    DOI: 10.1016/j.physa.2021.126605
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