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

## TL;DR

This paper demonstrates a thermodynamic equivalence between two-dimensional imperfect attractive Fermi gases and repulsive Bose gases, revealing that their thermodynamics are identical under certain conditions despite different particle statistics.

## Contribution

It establishes a precise thermodynamic equivalence between 2D imperfect attractive Fermi gases and repulsive Bose gases, including the case of ideal Bose gas.

## Key findings

- Thermodynamics of 2D imperfect Fermi gas remains well-defined for certain attraction strengths.
- Thermodynamics of Fermi and Bose gases are identical when specific interaction parameters are matched.
- At maximum attraction, the Fermi gas thermodynamics coincide with that of an ideal Bose gas.

## 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 $d=2$ imperfect Fermi gas remains well defined for $0 \leq a_{F}\leq a_{0}=h^2/2\pi m$, 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.