Statistical Potential for Identical Fermions: Emergent Attraction and Pauli Crystal Formation

TL;DR

This paper reveals that the collective statistical potential among identical fermions can become attractive for three or more particles, leading to Pauli crystal formations and complex thermodynamic behaviors.

Contribution

It demonstrates the emergence of attractive interactions and Pauli crystals from the collective potential, extending understanding beyond two-fermion systems.

Findings

The statistical potential becomes attractive for N≥3 fermions.

Pauli crystal configurations correspond to minima of the potential.

The system exhibits melting transitions at specific temperatures.

Abstract

We show that the thermodynamics of $N$ identical fermions maps onto that of distinguishable particles governed by a collective statistical potential -- the microscopic origin of degeneracy pressure. Known to be purely repulsive for ${N=2}$, this potential develops attractive contributions for ${N\geq 3}$. Its minima coincide with Pauli crystal configurations, providing the energetic origin of these structures. For large $N$, the dominant force is attractive on inner shells and repulsive on outer ones -- not of two-body origin. The global minimum undergoes discrete melting transitions at specific temperatures.