In this paper, we calculate the equations of state and the thermodynamic quantities for two- and three-dimensional hard-sphere Bose and Fermi gases in finite-size containers. The approach we used to deal with interacting gases is to convert the effect of interparticle hard-sphere interaction to a kind of boundary effect, and then the problem of a confined hard-sphere quantum gas is converted to the problem of a confined ideal quantum gas with a complex boundary. For this purpose, we first develop an approach for calculating the boundary effect on d-dimensional ideal quantum gases and then calculate the equation of state for confined quantum hard-sphere gases. The thermodynamic quantities and their low-temperature and high-density expansions are also given. In higher-order contributions, there are cross terms involving both the influences of the boundary and of the interparticle interaction. We compare the effect of the boundary and the effect of the interparticle interaction. Our result shows that, at low temperatures and high densities, the ratios of the effect of the boundary to the effect of the interparticle interaction in two dimensions are essentially different to those in three dimensions: in two dimensions, the ratios for Bose systems and for Fermi systems are the same and are independent of temperatures, while in three dimensions, the ratio for Bose systems depends on temperatures, but the ratio for Fermi systems is independent of temperatures. Moreover, for three-dimensional Fermi cases, compared with the contributions from the boundary, the contributions from the interparticle interaction to entropies and specific heats are negligible.In this paper, we calculate the equations of state and the thermodynamic quantities for two- and three-dimensional hard-sphere Bose and Fermi gases in finite-size containers. The approach we used to deal with interacting gases is to convert the effect of interparticle hard-sphere interaction to a kind of boundary effect, and then the problem of a confined hard-sphere quantum gas is converted to the problem of a confined ideal quantum gas with a complex boundary. For this purpose, we first develop an approach for calculating the boundary effect on d-dimensional ideal quantum gases and then calculate the equation of state for confined quantum hard-sphere gases. The thermodynamic quantities and their low-temperature and high-density expansions are also given. In higher-order contributions, there are cross terms involving both the influences of the boundary and of the interparticle interaction. We compare the effect of the boundary and the effect of the interparticle interaction. Our result shows that, at low temperatures and high densities, the ratios of the effect of the boundary to the effect of the interparticle interaction in two dimensions are essentially different to those in three dimensions: in two dimensions, the ratios for Bose systems and for Fermi systems are the same and are independent of temperatures, while in three dimensions, the ratio for Bose systems depends on temperatures, but the ratio for Fermi systems is independent of temperatures. Moreover, for three-dimensional Fermi cases, compared with the contributions from the boundary, the contributions from the interparticle interaction to entropies and specific heats are negligible.

Journal of Mathematical PhysicsDec 1, 200739 citations

Thermodynamics of Fermi Gases

Frédéric Chevy, Ch Salomon

Lecture notes in physicsOct 19, 20116 citations

Thermodynamic equivalence of two-dimensional imperfect attractive Fermi and repulsive Bose gases

Marek Napiórkowski, J. Piasecki

We consider two-dimensional imperfect attractive Fermi and repulsive Bose gases consisting of spinless point particles whose total interparticle interaction energy is represented by $a{N}^{2}/2V$ with $a=\ensuremath{-}{a}_{F}\ensuremath{\le}0$ for fermions and $a={a}_{B}\ensuremath{\ge}0$ for bosons. We show that, in spite of the attraction, the thermodynamics of a $d=2$ imperfect Fermi gas remains well defined for $0\ensuremath{\le}{a}_{F}\ensuremath{\le}{a}_{0}={h}^{2}/2\ensuremath{\pi}m$, and is exactly the same as the one of the repulsive imperfect Bose gas with ${a}_{B}={a}_{0}\ensuremath{-}{a}_{F}$. In particular, for ${a}_{F}={a}_{0}$ one observes the thermodynamic equivalence of the attractive imperfect Fermi gas and the ideal Bose gas.We consider two-dimensional imperfect attractive Fermi and repulsive Bose gases consisting of spinless point particles whose total interparticle interaction energy is represented by $a{N}^{2}/2V$ with $a=\ensuremath{-}{a}_{F}\ensuremath{\le}0$ for fermions and $a={a}_{B}\ensuremath{\ge}0$ for bosons. We show that, in spite of the attraction, the thermodynamics of a $d=2$ imperfect Fermi gas remains well defined for $0\ensuremath{\le}{a}_{F}\ensuremath{\le}{a}_{0}={h}^{2}/2\ensuremath{\pi}m$, and is exactly the same as the one of the repulsive imperfect Bose gas with ${a}_{B}={a}_{0}\ensuremath{-}{a}_{F}$. In particular, for ${a}_{F}={a}_{0}$ one observes the thermodynamic equivalence of the attractive imperfect Fermi gas and the ideal Bose gas.

arXiv:1705.09511Physical Review AJun 29, 20179 citations

We consider two-dimensional imperfect attractive Fermi and repulsive Bose gases consisting of spinless point particles whose total interparticle interaction energy is represented by

a{N}^{2}/2V

with $a=\ensuremath{-}{a}_{F}\ensuremath{\le}0$ for fermions and $a={a}_{B}\ensuremath{\ge}0$ for bosons. We show that, in spite of the attraction, the thermodynamics of a

d=2

imperfect Fermi gas remains well defined for $0\ensuremath{\le}{a}_{F}\ensuremath{\le}{a}_{0}={h}^{2}/2\ensuremath{\pi}m$, and is exactly the same as the one of the repulsive imperfect Bose gas with ${a}_{B}={a}_{0}\ensuremath{-}{a}_{F}$. In particular, for

{a}_{F}={a}_{0}

one observes the thermodynamic equivalence of the attractive imperfect Fermi gas and the ideal Bose gas.