Asymptotic expansions for the thermodynamic functions of an ideal Fermi gas are obtained about the point $z=1$ , where $z$ is the fugacity. We do this in three dimensions for the three different types of single-particle energy spectra, namely nonrelativistic, relativistic, and massless. To relate to liquid- $^{3}\mathrm{He}$ films, we also study the nonrelativistic spectrum in two dimensions.Asymptotic expansions for the thermodynamic functions of an ideal Fermi gas are obtained about the point $z=1$, where $z$ is the fugacity. We do this in three dimensions for the three different types of single-particle energy spectra, namely nonrelativistic, relativistic, and massless. To relate to liquid-$^{3}\mathrm{He}$ films, we also study the nonrelativistic spectrum in two dimensions.

Physical Review AOct 1, 19757 citations

The d-dimensional Landsberg gas

Jeremy Dunning-Davies

Expressions based on a recently proposed approximate density of states function are derived for thermodynamic functions of an ideal relativistic Bose gas in d dimensions. The results obtained are compared with those found using the exact density of states and agreement is found to be good in the three-dimensional case but less good in higher dimensions. It is noted that, in the extreme relativistic and non-relativistic limits, results agree exactly and, in the vicinity of the state of zero kinetic energy, the two densities of states exhibit smaller behaviour. Mention is made also of the application of this approximate density of states function to a consideration of the ideal relativistic Fermi gas.Expressions based on a recently proposed approximate density of states function are derived for thermodynamic functions of an ideal relativistic Bose gas in d dimensions. The results obtained are compared with those found using the exact density of states and agreement is found to be good in the three-dimensional case but less good in higher dimensions. It is noted that, in the extreme relativistic and non-relativistic limits, results agree exactly and, in the vicinity of the state of zero kinetic energy, the two densities of states exhibit smaller behaviour. Mention is made also of the application of this approximate density of states function to a consideration of the ideal relativistic Fermi gas.

Journal of Physics A Mathematical and GeneralNov 1, 19817 citations

Thermodynamic property of a relativistic Fermi gas trapped in hard-sphere potential

Fan Zhao-Lan, Men Fu-Dian, Dou Rui-Bo +1 more

Using the methods of numerical simulation and quantum statistics, based on the thermodynamic quantities of Fermi gas trapped in a general external potential, we studied the thermodynamic properties of a relativistic Fermi gas trapped in hard-sphere potential, gave the analytical expressions of the energy and heat capacity of the relativistic Fermi system, and analyzed the influence of the relativistic effect on the energy and heat capacity. The results showed the energy and heat capacity of the relativistic Fermi system is larger than those of the nonrelativistic case. The larger the relativistic eigenvalue, the lower the change temperature of heat capacity. As the temperature rises, the larger the relativistic eigenvalue, the greater the energy.Using the methods of numerical simulation and quantum statistics, based on the thermodynamic quantities of Fermi gas trapped in a general external potential, we studied the thermodynamic properties of a relativistic Fermi gas trapped in hard-sphere potential, gave the analytical expressions of the energy and heat capacity of the relativistic Fermi system, and analyzed the influence of the relativistic effect on the energy and heat capacity. The results showed the energy and heat capacity of the relativistic Fermi system is larger than those of the nonrelativistic case. The larger the relativistic eigenvalue, the lower the change temperature of heat capacity. As the temperature rises, the larger the relativistic eigenvalue, the greater the energy.

Acta Physica SinicaJan 1, 20103 citations

Thermodynamics of a Strongly-Interacting Fermi Gas

Joseph M. Kinast

APSMay 1, 20052 citations

Asymptotic expansions for the thermodynamic functions of an ideal Fermi gas are obtained about the point

z=1

, where

z

is the fugacity. We do this in three dimensions for the three different types of single-particle energy spectra, namely nonrelativistic, relativistic, and massless. To relate to liquid-

^{3}\mathrm{He}

films, we also study the nonrelativistic spectrum in two dimensions.