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Joined 2026-09-21 Message
Incoming links: John Hasbrouck Van Vleck
Anderson localization 2026-10-18
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.[ref]
Absence of Diffusion in Certain Random Lattices by Philip Warren Anderson. Anderson, 1958, pp.1492–1494, Sections I–II
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.[ref]
Local Moments and Localized States by Philip Warren Anderson. Local Moments and Localized States, pp.376–377,395–396; inspected institutional mirror www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics71-80-2.pdf
John Hasbrouck Van Vleck developed quantum mechanics explanations of magnetic susceptibility, including its temperature dependence; this is a distinct contribution from Anderson localization.[ref]
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 www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics71-80-2.pdf
Nobel Prize in Physics in 1977 2026-10-18
Awarded in equal shares to Philip Warren Anderson, Nevill Francis Mott and John Hasbrouck Van Vleck for theoretical investigations of electronic structure in magnetic and disordered systems.[ref]
The Nobel Prize in Physics 1977 by Nobel Prize Outreach. Three individual official laureate records: each one-third, same electronic-structure/magnetic/disordered-system motivation.