Fermi-Dirac Integrals in Degenerate Regimes: Novel Asymptotic Expansion

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2FCZ______%3A_____%2F24%3AN0000055" target="_blank" >RIV/CZ______:_____/24:N0000055 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10773-024-05695-8" target="_blank" >https://link.springer.com/article/10.1007/s10773-024-05695-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10773-024-05695-8" target="_blank" >10.1007/s10773-024-05695-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Fermi-Dirac Integrals in Degenerate Regimes: Novel Asymptotic Expansion

Popis výsledku v původním jazyce

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. We also improve on the understanding of the Sommerfeld expansion in the regime where the chemical potential is close to the mass and also in the high temperature regime. In these calculcations we use a novel characterization of the Fermi distribution allowing the separation of the finite and zero temperature phenomena. 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.

Název v anglickém jazyce

Fermi-Dirac Integrals in Degenerate Regimes: Novel Asymptotic Expansion

Popis výsledku anglicky

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. We also improve on the understanding of the Sommerfeld expansion in the regime where the chemical potential is close to the mass and also in the high temperature regime. In these calculcations we use a novel characterization of the Fermi distribution allowing the separation of the finite and zero temperature phenomena. 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.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

—

OECD FORD obor

10308 - Astronomy (including astrophysics,space science)

Projekt

—

Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Theoretical Physics

ISSN

0020-7748

e-ISSN

1572-9575

Svazek periodika

63

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

30

Strana od-do

163 (1-30)

Kód UT WoS článku

001262287600002

EID výsledku v databázi Scopus

2-s2.0-85197540909