A solvable model of a one-dimensional quantum gas with pair interaction

TL;DR

This paper introduces an exactly solvable one-dimensional quantum gas model with pair interactions, demonstrating how pairs form and behave similarly to bosons at low temperatures, with applications to thermodynamic properties.

Contribution

It presents a new solvable model for a 1D quantum gas with pair interactions, bridging fermionic/bosonic systems and ideal Bose gas behavior at low temperatures.

Findings

Pairs behave like pseudo-bosons at low temperatures

Model accurately describes specific heat and entropy for small systems

Thermodynamic limit can be analyzed with scaled harmonic potential

Abstract

We propose a solvable model of a one-dimensional harmonic oscillator quantum gas of two sorts of particles, fermions or bosons, which allows to describe the formation of pairs due to a suitable pair interaction. These pairs we call "pseudo-bosons" since the system can be approximated by an ideal bose gas for low temperatures. We illustrate this fact by considering the specific heat and the entropy function for N=8 pairs. The model can also be evaluated in the thermodynamic limit if the harmonic oscillator potential is suitable scaled.