Anderson Localization
3D tight-binding model — mobility edge & participation ratio
Parameters
Disorder W/t:
2.0
System size N:
20
Hopping t:
1.0
New Disorder Realization
Anderson (1958):
At W/t > W_c ≈ 16.5 (3D):
ALL states localized
Below W_c: mobility edge E_c
separates extended (|E|<E_c)
from localized (|E|>E_c)
PR = (Σ|ψ|⁴)⁻¹
Extended: PR ~ N
Localized: PR ~ const