| speaker: | Frithjof Anders Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, GERMANY |
| time: | Mo. 31.03.03, 16:00 - 17:00 |
We give an overview on a skeleton expansion for an impurity with internal degrees of freedom based upon a resolvent perturbation theory. The occurring self-energies are obtained by a generating functional. The lowest order approximation in $O(1/N)$ - $N$ is local spin degeneracy, the so-called non-crossing approximation (NCA), is defined by a simple set of integral equations which are analytically solvable at $T=0$. We make connection to the popular auxiliary particle approach, which leads to the same set of equations. The NCA captures already the essentials of the Kondo-Problem such as correct low-energy scale $T_K$, the Kondo-resonance close to the Fermi energy and non-Fermi liquid dynamics for multi-channel models. We show, how the method is extended to finite $U$, to non-equilibrium problems and to $O(1/N^2)$. Impurities in more complicated crystal-electric field environment can be treated.