Thermodynamic characteristics of ideal quantum gases in harmonic potentials within exact and semiclassical approaches
arXiv:2110.03359 · doi:10.1016/j.physa.2021.126605
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.
8 pages, 7 figures, published version