Phase diagram
C → K → F → U
C — Compression
Electron density n falling. Phase space of trajectories compresses. Positional correlations grow.
Drive parameter r_s
rs = potential/kinetic 12.0
Temperature T (normalised) 1.00
B field (Landau suppression) 0.0
Contact normal form · Chapter W
| Parameter | Symbol | Value |
|---|---|---|
| Transverse Lyapunov | μmax | −0.31 |
| Limit cycle freq. | ω | 0.19 |
| Decay constant | β | 1.7 |
| Critical threshold | rs* | ≈ 30–40 |
| Lattice geometry | — | Triangular / moiré |
Theorem W.1
The Wigner crystallization is G = U∘F∘K∘C acting on the 2D electron gas manifold X. At rs = rs* ≈ 30–40, the Jacobian loses rank by 1 (translational mode softens). The triangular lattice is the stable fixed point of the dm³ flow.