We investigate how two-particle interactions affect the electronic transport
through meso- and nanoscopic systems of two different types: quantum dots with
local Coulomb correlations and quasi one-dimensional quantum wires of
interacting electrons. A recently developed functional renormalization group
scheme is used that allows to investigate systems of complex geometry.
Considering simple setups we show that the method includes the essential
aspects of Luttinger liquid physics (one-dimensional wires) as well as of the
physics of local correlations, with the Kondo effect being an important
example. For more complex systems of coupled dots and Y-junctions of
interacting wires we find surprising new correlation effects.Comment: to appear in "Advances in Solid State Physics" Volume 46, Ed. R. Haug
(Springer, 2006