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

Theory of a Lattice Bose Gas

Toshiyuki Nishiyama, Masahisa Fukushima, Shokichi Kanno

Jan 1, 19690 citations

ON THE THERMODYNAMICS OF THE BOSE GAS

Yu.B. Rumer

Zhur. Eksptl'. i Teoret. Fiz.Sep 1, 19500 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.