2026/05/31 by Kawon Lee, Sangeun Oh, Young Woo Choi +1
Physics and Astronomy · #cond-mat.stat-mech
16 + 14 (SI) pages; 5 + 14 (SI) figures. v2: substantially revised, extended, and retitled (v1 title: "Statistical Potential for Identical Fermions: Emergent Attraction and Pauli Crystal Formation"). Code: https://github.com/Jeong24th/statistical_potential
arxiv created 2026/08/06 · arxiv updated 2026/08/07
Exchange statistics endows identical particles with an effective "statistical potential", whose familiar exact form is two-body and purely repulsive for fermions. Here we construct an exact collective many-body form: the thermodynamics of N trapped ideal fermions maps onto classical distinguishable particles governed by a single potential -- exactly for harmonic confinement at all temperatures, and to leading semiclassical order for arbitrary potentials. The associated force separates canonically into pairwise contributions, which for N≥ 3 can turn attractive, governed by a simple geometric criterion. Classical minimization reproduces observed few-body Pauli-crystal symmetries and agrees with the N=55 ground-state probability maximum at sub-percent shell accuracy. Heating drives discrete structural transitions accompanied by a crossover of the strongest force from attractive to repulsive. Both the potential and its forces are directly computable from existing single-shot imaging data, turning quantum exchange into measurable classical mechanics.