On the Anderson localization conjecture in Dusty Plasma

In 1958, Anderson suggested that sufficiently large impurities in a semi-conductor could lead to spatial localization of electrons. This idea unfolded into the field of Anderson Localization, one of the most fascinating phenomena in solid-state physics as it plays a major role in the conductive properties of imperfectly ordered materials. The \textit{Anderson Localization Conjecture} claims that random disorder of any strength causes localization of electrons in the medium. The problem has proven to be highly non-trivial. Over the years the community has argued whether spatial localization occurs in 2D for small impurities. From a mathematical standpoint, the conjecture is still considered an open question. In 2013, Liaw challenged the commonly held assumption that localization holds in 2D by introducing a new mathematically more rigorous method to test for extended states, and applying it to the discrete random Schr\"{o}dinger operator. One of the advantages of the underlying method is its versatility. It can be applied to any ordered system such as colloids, crystals, and atomic lattices. In a cross-disciplinary effort we merge this method with a numerical code used to simulate 2D physics systems, in preparation for experimentally testing the theory against complex plasma crystals.