Liquid Crystal Defect Coarsening — Kibble-Zurek Mechanism

Topological defect density n(t) ~ t^(−1) · coarsening; Kibble-Zurek: n ~ τ_Q^(−ν/(1+νz))

Time step0

Defect count—

Defect density—

Coarsening ξ—

Noise T 0.3

Quench rate fast

Kibble-Zurek mechanism: When a system is quenched through a continuous phase transition at finite rate τ_Q, the correlation length ξ̂ = ξ₀(τ_Q/τ₀)^(ν/(1+νz)) sets the initial defect density n₀ ~ ξ̂^(−d). For a 2D nematic: defects are ±½ disclinations. The order parameter is θ ∈ [0,π) (head-tail symmetry). Coarsening follows n(t) ~ t^(−1) (Allen-Cahn/Kibble scaling). Colors encode director angle; winding numbers ±½ shown as bright spots.