Abstract:
Despite decades of intensive studies, the formation of exponentially localized electron eigenstates, which prevent the electron transport to be possible in strongly disordered solids, is still not fully understood. In this seminar, planed as two-part, a proposal for a~mean-field theory of this disorder-driven metal-insulator transition will be referred.
In the first talk, response functions related to transport properties of non-interacting electrons in the presence of a random potential will be introduced. Subsequently, the averaging over disorder configurations, which makes the system under investigation effectively translationally invariant but correlated (interacting), will be performed. Ward identities will help to establish a close relationship between electrical conductivity and diffusion. Such a relation is substantial, since it allows to calculate conductivity, the quantity of experimental interest, via a physical process that is easier to access theoretically - the diffusive relaxation of inhomogeneities in the particle density.