Density of States for the Unitary Fermi Gas and the Schwarzschild Black Hole

Year: 2023

Authors: Salasnich Luca

Autors Affiliation: Univ Padua, Dipartimento Fis & Astron Galileo Galilei & Padua, Via Marzolo 8, I-35131 Padua, Italy; Consiglio Nazl Ric CNR, Ist Nazl Ott INO, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy; Ist Nazl Fis Nucl INFN, Sez Padova, Via Marzolo 8, I-35131 Padua, Italy.

Abstract: The density of states of a quantum system can be calculated from its definition, but, in some cases, this approach is quite cumbersome. Alternatively, the density of states can be deduced from the microcanonical entropy or from the canonical partition function. After discussing the relationship among these procedures, we suggest a simple numerical method, which is equivalent in the thermodynamic limit to perform a Legendre transformation, to obtain the density of states from the Helmholtz free energy. We apply this method to determine the many-body density of states of the unitary Fermi gas, a very dilute system of identical fermions interacting with a divergent scattering length. The unitary Fermi gas is highly symmetric due to the absence of any internal scale except for the average distance between two particles and, for this reason, its equation of state is called universal. In the last part of the paper, by using the same thermodynamical techniques, we review some properties of the density of states of a Schwarzschild black hole, which shares the problem of finding the density of states directly from its definition with the unitary Fermi gas.

Journal/Review: Symmetry-Basel

Volume: 15 (2)      Pages from: 350-1  to: 350-12

KeyWords: density of states; unitary Fermi gas; entropy; black holes; free energy
DOI: 10.3390/sym15020350

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