Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Thermodynamic functions of an ideal Fermi gas in the intermediate quantum region

S. R. Hore, Norman E. Frankel

Published Oct 1, 1975• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.12.1617

Related papers

Thermodynamic functions in the intermediate quantum region of an ideal Fermi gas in a weak magnetic field

S. R. Hore, Norman E. Frankel

Asymptotic expansions for the thermodynamic functions of an ideal spin-\textonehalf{} Fermi gas in a weak magnetic field are obtained about the point $z=1$, where $z$ is the fugacity. We consider paramagnetism, diamagnetism, and paramagnetism plus diamagnetism together. To relate to liquid $^{3}\mathrm{He}$ films and bulk fluid, we study the spin paramagnetism in two and three dimensions.

Physical Review A•Nov 1, 1975•1 citation

Quasiparticle spectra and the calculation of thermodynamics for a two-dimensional Fermi liquid

Dermot Coffey

If the dynamical quasiparticle spectrum of a Fermi liquid (FL), ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$, given by the poles of the single-particle propagator, is used in the expression for the entropy of a noninteracting Fermi gas, one finds that the result is different from that calculated directly from the thermodynamic potential. In particular, the coefficient of the ${\mathit{T}}^{3}$lnT terms, the leading correction to the linear T dependence for a three-dimensional (3D) FL, is overestimated when calculated from ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$. The thermodynamic properties may be calculated correctly from a second quasiparticle spectrum, the statistical quasiparticle spectrum, ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{st}}$. In this paper I calculate the corrections to leading linear energy and temperature dependences for a 2D FL. I compare the difference between the two spectra in the 2D and 3D cases. Although these differences are qualitatively the same, they are quantitatively larger in the 2D case.

Physical review. B, Condensed matter•May 15, 1995•1 citation

Thermodynamic coefficients of ideal Fermi gas

Alexey Kozharin, Pavel R. Levashov

Abstract We present analytical formulae for the first and second derivatives of the Helmholtz free energy of non‐relativistic ideal Fermi gas. Important thermodynamic quantities such as heat capacity, sound velocity, heat capacity ratio, and others are explicitly expressed through the derivatives. We demonstrate correct ideal Boltzmann gas and low‐temperature Fermi gas asymptotes and derive corrections to thermodynamic functions for these limiting cases. Numerical computations of thermodynamic properties of ideal Fermi gas can be accurately performed using the developed freely available Python module ifg.

arXiv:2012.06741•Contributions to Plasma Physics•Oct 1, 2021•3 citations

Thermodynamics of the nonrelativistic free-electron Fermi gas in one, two, and three dimensions from the degenerate to the nondegenerate temperature regime

D. C. Johnston

The thermodynamic properties of a nonrelativistic free-electron Fermi gas is of fundamental interest in condensed matter physics. Properties previously studied in three-dimensions (3D) in the low- and high-temperature limits include the internal energy, heat capacity, zero-field magnetic spin susceptibility, and pressure. Here we report solutions for the temperature dependence spanning these two temperature regimes of the chemical potential, internal energy, magnetic susceptibility, and the heat capacity at constant volume in 1D, 2D, and 3D. Also calculated are the pressure, enthalpy, heat capacity at constant pressure, isothermal compressibility, and thermal expansion coefficient versus temperature in 2D and 3D. Of primary interest here are the detailed dimension-dependent crossovers of these properties between the degenerate and nondegenerate temperature regime, which are graphically illustrated for each of the above properties.

arXiv:2012.07663•Dec 14, 2020•1 citation

Quantum Statistics of Ideal Gases in Two Dimensions

Robert Mccredie May

It is shown that in two dimensions the specific heat ${C}_{V}(T, N)$ for an ideal gas of Fermi particles is identical with that for an ideal Bose gas for all $T$ and $N$. This is true despite the great difference in the distribution functions of the two systems at low temperatures. To shed further light on this identity, the quantum statistics of ideal gases are investigated treating the number of dimensions as a continuous variable: $n=2$ is seen to be a special case. In the extreme relativistic region, the analogous special case is $n=1$.

Physical Review•Sep 14, 1964•96 citations

Unitary Fermi gas in the epsilon expansion

Yusuke Nishida

We construct systematic expansions around four and two spatial dimensions for a Fermi gas near the unitarity limit. Near four spatial dimensions such a Fermi gas can be understood as a weakly-interacting system of fermionic and bosonic degrees of freedom. To the leading and next-to-leading orders in the expansion over ε=4-d, with d being the dimensionality of space, we determine the thermodynamic functions, the fermion quasiparticle spectrum, the critical polarizations, and the critical temperature as functions of the binding energy of the two-body state. We also show that the unitary Fermi gas near two spatial dimensions reduces to a weakly-interacting Fermi gas and calculate the thermodynamic functions and the fermion quasiparticle spectrum in the expansion over \barε=d-2. We discuss the matching of the two systematic expansions around four and two spatial dimensions in order to extract physical observables at d=3. We find good agreement of the results with those from recent Monte Carlo simulations.

arXiv:cond-mat/0703465•Mar 19, 2007•2 citations
Asymptotic expansions for the thermodynamic functions of an ideal Fermi gas are obtained about the point z=1z=1z=1, where zzz 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-3He^{3}\mathrm{He}3He films, we also study the nonrelativistic spectrum in two dimensions.
Asymptotic expansions for the thermodynamic functions of an ideal spin-\textonehalf{} Fermi gas in a weak magnetic field are obtained about the point z=1z=1z=1, where zzz is the fugacity. We consider paramagnetism, diamagnetism, and paramagnetism plus diamagnetism together. To relate to liquid 3He^{3}\mathrm{He}3He films and bulk fluid, we study the spin paramagnetism in two and three dimensions.
If the dynamical quasiparticle spectrum of a Fermi liquid (FL), ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$, given by the poles of the single-particle propagator, is used in the expression for the entropy of a noninteracting Fermi gas, one finds that the result is different from that calculated directly from the thermodynamic potential. In particular, the coefficient of the T3{\mathit{T}}^{3}T3lnT terms, the leading correction to the linear T dependence for a three-dimensional (3D) FL, is overestimated when calculated from ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$. The thermodynamic properties may be calculated correctly from a second quasiparticle spectrum, the statistical quasiparticle spectrum, ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{st}}$. In this paper I calculate the corrections to leading linear energy and temperature dependences for a 2D FL. I compare the difference between the two spectra in the 2D and 3D cases. Although these differences are qualitatively the same, they are quantitatively larger in the 2D case.
Abstract We present analytical formulae for the first and second derivatives of the Helmholtz free energy of non‐relativistic ideal Fermi gas. Important thermodynamic quantities such as heat capacity, sound velocity, heat capacity ratio, and others are explicitly expressed through the derivatives. We demonstrate correct ideal Boltzmann gas and low‐temperature Fermi gas asymptotes and derive corrections to thermodynamic functions for these limiting cases. Numerical computations of thermodynamic properties of ideal Fermi gas can be accurately performed using the developed freely available Python module ifg.
The thermodynamic properties of a nonrelativistic free-electron Fermi gas is of fundamental interest in condensed matter physics. Properties previously studied in three-dimensions (3D) in the low- and high-temperature limits include the internal energy, heat capacity, zero-field magnetic spin susceptibility, and pressure. Here we report solutions for the temperature dependence spanning these two temperature regimes of the chemical potential, internal energy, magnetic susceptibility, and the heat capacity at constant volume in 1D, 2D, and 3D. Also calculated are the pressure, enthalpy, heat capacity at constant pressure, isothermal compressibility, and thermal expansion coefficient versus temperature in 2D and 3D. Of primary interest here are the detailed dimension-dependent crossovers of these properties between the degenerate and nondegenerate temperature regime, which are graphically illustrated for each of the above properties.
It is shown that in two dimensions the specific heat CV(T,N){C}_{V}(T, N)CV​(T,N) for an ideal gas of Fermi particles is identical with that for an ideal Bose gas for all TTT and NNN. This is true despite the great difference in the distribution functions of the two systems at low temperatures. To shed further light on this identity, the quantum statistics of ideal gases are investigated treating the number of dimensions as a continuous variable: n=2n=2n=2 is seen to be a special case. In the extreme relativistic region, the analogous special case is n=1n=1n=1.
We construct systematic expansions around four and two spatial dimensions for a Fermi gas near the unitarity limit. Near four spatial dimensions such a Fermi gas can be understood as a weakly-interacting system of fermionic and bosonic degrees of freedom. To the leading and next-to-leading orders in the expansion over ε=4-d, with d being the dimensionality of space, we determine the thermodynamic functions, the fermion quasiparticle spectrum, the critical polarizations, and the critical temperature as functions of the binding energy of the two-body state. We also show that the unitary Fermi gas near two spatial dimensions reduces to a weakly-interacting Fermi gas and calculate the thermodynamic functions and the fermion quasiparticle spectrum in the expansion over \barε=d-2. We discuss the matching of the two systematic expansions around four and two spatial dimensions in order to extract physical observables at d=3. We find good agreement of the results with those from recent Monte Carlo simulations.