Anderson localization

Anderson localization is the suppression of wave transport by disorder: interference among multiply scattered waves confines states in space. It can occur for electrons, light, sound, and other waves.

Multiple scattering: Repeated deflections of a wave by inhomogeneities in a medium. Disorder repeatedly scatters waves, creating the paths whose interference produces localization.
Disorder (physics): Spatial randomness in the structure or properties of a physical system. Random potentials or material variations provide the scattering landscape that can localize waves.
Philip W. Anderson: An American physicist whose work on disordered systems helped establish condensed-matter physics. His 1958 paper showed that disorder can prevent electron diffusion without interactions.
Disordered conductors: Materials whose electrical properties vary randomly across space. Their resistance can rise dramatically when electronic states become localized.
Weak localization: A perturbative reduction of conductivity caused by interference between time-reversed paths. It is a precursor correction to transport, not necessarily complete exponential confinement.
Quantum interference: The addition of quantum amplitudes can enhance or suppress the probability of an outcome. Scattered paths interfere, reducing transport when their phases reinforce return toward the starting region.
Tight-binding model: A model of particles moving between localized sites with specified hopping amplitudes. Random site energies or hopping strengths make localization mathematically tractable.
Anderson's 1958 paper: Philip W. Anderson's paper introducing localization of electronic states in disordered lattices. It framed localization as a consequence of disorder and quantum mechanics.
Photonic crystal: A periodic optical material with a photonic band structure that controls light propagation. Periodic band gaps can confine light without the disorder mechanism of Anderson localization.
Many-body localization: A proposed or realized failure of interacting quantum systems to reach thermal equilibrium because of disorder. It extends localization to interacting systems, where the issue includes thermalization.

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