ABSTRACT
This chapter examines how to generalize the scattering matrix formalism to include the effect of electron–electron interactions. Electrons propagating in a metal get scattered every time they approach any kind of obstacle, which can be, for example, an impurity, a boundary imperfection, and a tunnel barrier. The chapter provides complete information about transport properties of a coherent scatterer in the presence of electron–electron interactions. The concept of full counting statistics (FCS) plays an important role in modern theory of quantum transport. On one hand, there exists a relatively simple and elegant theoretical formulation of FCS in terms of the cumulant-generating function, which allows to fully account for fundamental issues such as quantum coherent electron scattering and Pauli principle. On the other hand, first several current cumulants can be reliably detected in modern experiments thereby enabling one a detailed comparison between experimental results and theoretical predictions.
