On dynamical properties of electrons in Anderson-Mott insulators

Properties of electrons in non-crystalline (alias disordered) systems has been a very active research topic for over half a century, since Anderson's ground breaking paper on localization. In strongly disordered systems electrons become Anderson and Mott localized. Interactions become important because screening by localized electrons is ineffective. Dynamical theories for such systems have long been controversial. Nevertheless one theory came to prominence in the literature and is often invoked and/or used. It is shown here that that theory is unsatisfactory in several aspects. It is based on the one-particle density of states, which turns out to be irrelevant to the problem it addresses. Another shortcoming is an implicit conjecture that interacting electrons move independently of each other. The theory is also in questionable agreement with experiment. It is shown that two other theories are free of those problems. They are useful for different types of studies, are compatible with each other and in agreement with experiment.