Anderson Localization
P.W. Anderson (1958): disorder in a lattice can completely halt electron diffusion.
In 1D/2D: ALL states localize for any disorder.
In 3D: localization-delocalization transition at critical W.
Localization length: ξ ~ exp(2t/W)
IPR (inverse participation ratio):
Σ|ψ|⁴ → 1 (localized), 1/N (extended)
IPR: —
P.W. Anderson (1958): disorder in a lattice can completely halt electron diffusion.
In 1D/2D: ALL states localize for any disorder.
In 3D: localization-delocalization transition at critical W.
Localization length: ξ ~ exp(2t/W)
IPR (inverse participation ratio):
Σ|ψ|⁴ → 1 (localized), 1/N (extended)
IPR: —