Statistical Mechanical Interpretation of 2D Pauli Crystals

TL;DR

This paper provides a statistical mechanical framework to understand the formation of Pauli crystals in ultra-cold fermions confined in a 2D harmonic trap, unifying degeneracy and oscillator models.

Contribution

It introduces a novel statistical mechanical interpretation of Pauli crystals, combining fermion degeneracy and harmonic oscillator approaches for a comprehensive analysis.

Findings

Calculated energy and radius of fermion arrangements.

Unified two approaches for better description of Pauli crystals.

Enhanced understanding of non-interacting fermion configurations.

Abstract

A manifestation of the Pauli Exclusion Principle is observed when fermions are trapped in the ground state of a 2D harmonic oscillator trap at very low temperatures. This non-interaction of fermions results in the formation of Pauli crystals. This work introduces a statistical mechanical interpretation of the principles that led to the observation of Pauli crystals by calculating the energy, radius and other parameters of the non-interacting arrangement of ultra-cold fermions. This model approaches the problem from two different directions, namely fermion degeneracy and harmonic oscillator treatment. Unifying the two different approaches gives a more comprehensive and robust description of the various parameters of Pauli crystals.