Abstract

The phenomenon of Anderson loclaization was proposed 65 years ago to undertand the observed metal-insulator transition in electron conduction.  An “often quoted but never read work” according to Co-Nobel laureat Sir Nevil Mott, “an unregognizable monster” according to its creator Phillip Anderson after reviewing 25 years of intense research. The first mathematical proofs of Anderson loclization of electrons in 3D at low energies appeared in 1983. Many attemps to observe electron localization were conteststed. Numerical experiments – “indignified”  according to its creator, revealed Anderson localization, accompanied by critical behavior and finite-size scaling near the mobility edge. The first experiments with classical waves were done at the end of the former century, argued to be easier because free from dephasing and interaction. Localization of acoustic, elastic and micro waves has been reported, and recently even the 3D localization of cold atoms in light speckle. The observation of 3D light remains one of the holy grails. The sample needs to be one hundred million times denser than a fog with 1 meter visibility and this is challenging. A recent numercial experiments done with randomly positionned, resonant electric dipoles revealed no Anderson transition, not even for many dipoles packed together within a cubic wavelength, although this was widely believed to be  the simplest model to describe localization of light.  The vector nature of light, and in particular its non-propagating longitudical component is a very specific feature. Does it create another transport channel, so to prevent light to localize in this model? We will give an argument what breaks down in Anderson’s “Theory of White Paint”.