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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
Philip W. Anderson Created 2026-10-24 Updated 2026-11-05
Philip W. Anderson showed that disorder can prevent quantum transport in a lattice. His 1958 model assigns random energies to sites connected by hopping, demonstrating regimes in which diffusion fails even though motion between neighboring sites is allowed. The phenomenon now called Anderson localization depends on coherent wave propagation through a random system. It changed how an insulating response could be understood, connecting transport with the spatial character of quantum states.[ref]
Absence of Diffusion in Certain Random Lattices by Philip Warren Anderson. Physical Review 109, 1492 (1958), random-site model and absence-of-diffusion criterion
Portrait of Philip W. Anderson
. JdH; Yale University photograph, existing Commons crop. Creative Commons Attribution-ShareAlike 3.0 Unported selected from File's multiple available licenses; alternative GFDL/older CC licenses not needed., via Wikimedia Commons. Source.