Theory of inelastic scattering from quantum impurities

Details Theory of inelastic scattering from quantum impurities Theory of inelastic scattering from quantum impurities

2007-03-12

arxiv.org/abs/cond-mat/0703293v2

Phys. Rev. B 75, 235112 (2007)

Physics

Condensed Matter

Strongly Correlated Electrons

published version

Scientific paper

10.1103/PhysRevB.75.235112

We use the framework set up recently to compute non-perturbatively inelastic scattering from quantum impurities [G. Zar\'and {\it et al.}, Phys. Rev. Lett. {\bf 93}, 107204 (2004)] to study the 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 cross-over between the non-Fermi liquid and Fermi liquid regimes appears in 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.

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