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Anderson localization Created 2026-10-18 Updated 2026-10-20
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
John Hasbrouck Van Vleck Created 2026-10-18 Updated 2026-11-05
John Hasbrouck Van Vleck developed the quantum theory of magnetic response in atoms and solids. magnetic susceptibility depends on the spectrum and magnetic matrix elements of the system, not only on a classical picture of permanent dipoles. An applied field can admix excited states into the ground state and thereby change its energy and magnetic moment. His treatment connected atomic quantum mechanics, crystal fields and measured magnetism, explaining effects that a purely classical thermal average misses.[ref]
Quantum Mechanics: The Key to Understanding Magnetism by John Hasbrouck Van Vleck. Nobel lecture, atomic susceptibility and crystal-field magnetic response
A physicist.[ref]
Professional profile of John Hasbrouck Van Vleck. Independent professional identity
Portrait of John Hasbrouck Van Vleck
. Photograph by E.B. Boatner, courtesy AIP Emilio Segrè Visual Archives, Bainbridge Collection; American Institute of Physics (AIP); existing Commons crop by Artem.G. American Institute of Physics attribution-only permission, via Wikimedia Commons. Source.
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.