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

Marek Napiórkowski and Jarosław Piasecki

Phys. Rev. A 95, 063627 – Published 29 June 2017

Abstract

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