Characterizing Asymptotic Expansions of Quantum Fermi Gas
arxiv(2024)
摘要
We characterize in a novel manner the physical properties of the low
temperature Fermi gas in the degenerate domain as a function of temperature and
chemical potential. For the first time we obtain low temperature T results in
the domain where several fermions are found within a de Broglie spatial cell.
In this regime, the usual high degeneracy Sommerfeld expansion fails. The other
known semi-classical Boltzmann domain applies when fewer than one particle is
found in the de Broglie cell. The relative errors of the three approximate
methods (Boltzmann limit, Sommerfeld expansion, and the new domain of several
particles in the de Broglie cell) are quantified. In order to extend the
understanding of the Sommerfeld expansion, we developed a novel
characterization of the Fermi distribution allowing the separation of the
finite and zero temperature phenomena.
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