Perex
Abstract:
I worked as a Fulbright Scholar at Louisiana State University from November 2014 to June 2015. The main objective of the project was to make diagrammatic approximations for one and two-particle Green functions thermodynamically consistent for disordered and correlated electrons. The first seminar is devoted to a consistent description of charge diffusion in random lattices.
Text
To describe diffusion and its vanishing (Anderson localization) one needs to use nontrivial and self-consistent approximations for two-particle (vertex) functions. One particle Green functions enter the two-particle diagrammatic theory as an independent input. To reach thermodynamically consistent results we must, however, relate the one-electron self-energy and the two-particle irreducible vertex via a Ward identity. The latter cannot be guaranteed in the two-particle constructions. We show how to restore the dynamical Ward identity and all macroscopic conservation laws in the two-particle perturbation theory for non-interacting disordered electrons.