Confined Harmonically Interacting Spin-Polarised Fermions

TL;DR

This paper presents a path integral method to analyze the thermodynamic properties of harmonically interacting spin-polarized fermions confined in a three-dimensional parabolic potential, revealing scaling laws for key thermodynamic quantities.

Contribution

It introduces a novel path integral approach for calculating thermodynamics of confined fermions, demonstrating scaling behaviors across temperature and particle number.

Findings

Chemical potential and internal energy follow a scaling law.

Dependences are valid over the full range of temperature and particle number.

Method provides a new way to analyze confined quantum fermion systems.

Abstract

The thermodynamical properties are calculated for a three-dimensional model of $N$ harmonically interacting spin-polarized fermions in a parabolic potential well. The obtained dependences of the chemical potential and of the internal energy on the complete range of the temperature and of the number of particles turn out to obey a scaling law, similar to the scaling from the continuum approximation for the density of states. The calculation technique is based on our path integral approach of symmetrized density matrices for identical particles in a parabolic confining well.