Theory of inelastic scattering from quantum impurities

We use the framework setup recently to compute nonperturbatively inelastic scattering from quantum impurities [G. Zaránd et al., Phys. Rev. Lett. 93, 107204 (2004)] to study the energy dependence of the single-particle $S$ matrix and the inelastic scattering cross section for a number of quantum impurity models. We study the case of the spin $S=1∕2$ two-channel Kondo model, the Anderson model, and the usual $S=1∕2$ single-channel Kondo model. We discuss the difference between non-Fermi-liquid and Fermi-liquid models and study how a crossover between the non-Fermi-liquid and Fermi-liquid regimes appears in the case of channel anisotropy for the $S=1∕2$ two-channel Kondo model. We show that for the most elementary non-Fermi-liquid system, the two-channel Kondo model, half of the scattering remains inelastic even at the Fermi energy. Details of the derivation of the reduction formulas and a simple path integral approach to connect the $T$ matrix to local correlation functions are also presented.