If a nonmagnetic metal contains transition metal or rare earth impurities with partly filled inner shells the conductivity can show an anomalous low temperature behavior. The first step towards a theoretical understanding emerged when J. Kondo proposed a model in which the magnetic impurity is modeled by a localized spin coupled to the spin density of the metallic host at the impurity site, which is assumed to consist of noninteracting electrons. After a long history of early approximate solutions this model - as well as Anderson's single impurity model - was solved ``exactly'' using the numerical renormalization group (NRG) and the Bethe ansatz method. With lowering the temperature the asymptotically free spin is screened by the conduction electrons. Similar crossover behavior is found in quantum many-body systems in various other fields of physics. A special feature of the strong local electron correlations is the ``Kondo-resonance'' in the impurity spectral function which influences various measurable properties. Recently, a novel application of such ``quantum impurity systems'' to describe the electronic transport through artificial ``quantum dots'' has emerged, as such quantum dots can be modeled by single or multi-impurity systems.
While the equilibrium behavior of a single magnetic impurity is by now well understood this is not true for systems of several impurities and for the nonequilibrium properties. Both problems are attacked in our group using e.g. the NRG and the functional renormalization group for multi-impurity systems as well as the generalization of the latter to systems far from equilibrium.
Universal resistivity of Kondo impurities.