Anderson Localization — 1D Disordered System

In 1D, all eigenstates localize for any disorder (Anderson 1958). Transfer matrix method computes the exact wavefunction |ψ(x)|². The localization length ξ ≈ 105/(W²) for weak disorder. Watch exponential decay emerge.

Localization length ξ ≈ — sites  |  Lyapunov γ = —  |  In 1D/2D all states localize; 3D has metal-insulator transition