Wigner Crystal — Electron Localization
r_s = a/(a_B) · crystallization when r_s ≫ 1 · Coulomb vs kinetic energy
r_s = —
The Wigner crystal forms when the Coulomb repulsion energy dominates kinetic (zero-point) energy, i.e. when the Wigner-Seitz radius r_s ≫ 1 (in units of Bohr radius a_B). E_Coulomb ∼ e²/(ε a) ∝ r_s, E_kinetic ∼ ℏ²/(m a²) ∝ r_s⁻². Crystallization threshold: r_s ≈ 37 (3D), r_s ≈ 37 (2D, debated). The simulated electrons minimize total Coulomb energy in a circular jellium background, forming hexagonal lattices at large r_s.