Theory of inelastic scattering from quantum impurities

We use the framework setup recently to compute nonperturbatively inelastic scattering from quantum impurities G. Zarand et al., Phys. Rev. Lett. 93, 107204 2004 to study the energy dependence of the singleparticle 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 singlechannel 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.