Anderson Localization

Anderson 1958: Random on-site potential εᵢ ∈ [−W/2, W/2] localizes all eigenstates in 1D for any W > 0. Wavefunction |ψ(x)| ~ e^−|x|/ξ, ξ ~ (t/W)². IPR = Σ|ψᵢ|⁴: IPR → 1/N (extended), IPR → 1 (localized). Nobel Prize 1977.