Anderson localization is a metal-insulator transition caused by disorder. It has been connected to several phenomena such as conductivity of solids, transport of light and sound in random media, and the quantum Hall transition. The scaling theory of localization predicts that all states are localized in 1D and 2D disordered systems. In 3D there exists a transition point where the eigenstates are critical and have multifractal structure. I report how this multifractality has recently been observed in the Anderson transition of ultrasound in a 3D metal network. Furthermore, using analytic calculations and numerical simulations, I show that the propagation of electromagnetic polar waves in a 1D array of near-resonant scatterers also follows critical scaling behavior. This is caused by the long-range interaction between the scatterers, which is not treated by the scaling theory.
Seminar on Disorder and strong electron correlations: "Identifying the critical state of the Anderson localization transition with its multifractality"
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