Proof — Fröhlich–Spencer: Anderson localization for tight-binding models
Statement
For a class of Anderson tight-binding Hamiltonians on ℤ^d with d ≥ 3 and sufficiently small disorder (and standard assumptions on the single-site distribution), the spectrum is pure point and eigenfunctions are exponentially localized (with probability one in the disorder). Landmark rigorous proof of Anderson localization in the lattice setting. Proved in ZFC.
Source
J. Fröhlich, T. Spencer, Absence of diffusion in the Anderson tight binding model for large disorder or low energy, Commun. Math. Phys. 88 (1983), 151–184.
Domains
mathematics, physics
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