The 1958 model kept hopping but randomized energies
Anderson’s 1958 paper studied a lattice with site energies drawn from a random distribution. Neighboring sites remained coupled, but sufficiently strong randomness could prevent diffusion of a coherent quantum excitation.
The result challenged the assumption that disorder merely shortens a mean free path. A connected graph does not guarantee extended quantum eigenstates.
Interference distinguishes localization from a blocked path
Scattered amplitudes add with phase. Repeated coherent scattering can suppress long-range propagation without removing the geometric route. Turning off phase coherence or adding interactions changes the problem, even if the same random landscape remains.
Size and dimension matter to the inference
A finite sample can show low transmission through a barrier, a resonance mismatch or localization. Varying sample size and disorder distinguishes these possibilities. The existence and character of a mobility edge depend on dimension and symmetry, so one chain does not represent every material.
The existing Lab keeps the single-particle question
The localization Lab compares spatial confinement and transport in its specified coherent model. It is reused here rather than rebuilt. The 1977 contribution also includes local-moment physics; interaction-driven Mott insulation is discussed separately because it requires a different mechanism.