= Anderson localization
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<Anderson localization> is the confinement of <Electron> <wave functions>, or other <wave> modes, by <interference> between repeated <wave scattering> paths in static disorder. A <localized eigenstate> occupies a limited region even in a much larger sample. Disorder can therefore suppress <diffusion> without absorbing the <wave>. In 1958, <Philip Warren Anderson> studied random site <energies> and intersite coupling, finding a regime without transport. His paper develops a theoretical model; it does not report an Anderson laboratory measurement.<Absence of Diffusion in Certain Random Lattices by Philip Warren Anderson>[Anderson, 1958, pp.1492–1494, Sections I–II]{ref}
The distinction from ordinary <multiple scattering> is the retention of <wave phases>: alternative paths contribute <probability amplitudes> before their squared <modulus> is taken. Adding path probabilities alone loses the cross terms responsible for <interference>. This makes <Anderson localization> useful as a warning about transport models: repeated deflections need not produce unlimited <diffusion>. It also connects <Electron> transport with <wave propagation in a random medium>, although the detailed equations and experimental diagnostics differ between <Electrons>, <light> and <acoustic waves>.
<Philip Warren Anderson>'s 1977 lecture distinguishes localized magnetic moments from disorder-localized states. It credits <Nevill Francis Mott> with recognizing the significance of the <mobility edge>. A <Mott insulator> instead requires <Electron> interactions and can exist without disorder.<Local Moments and Localized States by Philip Warren Anderson>[Local Moments and Localized States, pp.376–377,395–396; inspected institutional mirror https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics71-80-2.pdf]{ref}
<John Hasbrouck Van Vleck> developed <quantum mechanics> explanations of <magnetic susceptibility>, including its <temperature> dependence; this is a distinct contribution from <Anderson localization>.<Quantum Mechanics: The Key to Understanding Magnetism by John Hasbrouck Van Vleck>[Quantum Mechanics: The Key to Understanding Magnetism, pp.355–356; inspected institutional mirror https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics71-80-2.pdf]{ref}
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