Confined Harmonically Interacting Spin-Polarized Fermions in a Magnetic Field: Thermodynamics

TL;DR

This paper explores how a magnetic field and harmonic interactions affect the thermodynamics of a finite system of spin-polarized fermions in a confining potential, extending previous path integral methods.

Contribution

It introduces a path integral approach to analyze thermodynamic properties of finite, harmonically interacting fermions under magnetic fields, including deviations from the thermodynamic limit.

Findings

Thermodynamic properties are calculated for small particle numbers.

Deviations from the thermodynamic limit are negligible for about 100 or more particles.

Scaling relations similar to the continuum density of states are observed even for smaller systems.

Abstract

We investigate the combined influence of a magnetic field and a harmonic interparticle interaction on the thermodynamic properties of a finite number of spin polarized fermions in a confiment potential. This study is an extension using our path integral approach of symmetrized density matrices for identical particles. The thermodynamical properties are calculated for a three dimensional model of N harmonically interacting spin polarized fermions in a parabolic potential well in the presence of a magnetic field. The free energy and the internal energy are obtained for a limited number of particles. Deviations from the thermodynamical limit become negligible for about 100 or more particles, but even for a smaller number of fermions present in the well, scaling relations similar to those of the continuum approximation to the density of states are already satisfied.