Topological Kink — φ⁴ Field Theory
Kink and antikink solitons in the double-well potential, kink-antikink scattering
Parameters
Mass m²:
1.00
Coupling λ:
1.00
Kink velocity v:
0.30
Kink separation d:
6.0
Damping γ:
0.00
Kink + Antikink
Single Kink
Reset
φ⁴ Lagrangian:
L = ½(∂_μφ)² − V(φ)
V(φ) = λ/4 (φ²−m²/λ)²
Kink solution:
φ_K(x) = (m/√λ) tanh[m(x−vt)/√(2γ_L)]
Mass:
M_K = 2√2 m³/(3λ)
Topological charge:
Q = (λ/2m)∫∂_xφ dx = ±1
After collision, kinks can reflect, form bound states (bions), or annihilate. The critical velocity separates these regimes.