Anderson Localization
Random on-site disorder localizes all quantum states in 1D. Wavefunctions decay exponentially: |ψₙ|² ~ e−|n−n₀|/ξ. No diffusion for any disorder strength.
Hamiltonian: H = Σᵢ εᵢ|i⟩⟨i| − t(|i⟩⟨i+1| + h.c.), εᵢ ~ Uniform[−W/2, W/2], hopping t=1.
Localization length: ξ ≈ 105t²/W² (Born approx., 1D). Gold envelope fits e−|n−peak|/ξ.