Theory of inelastic scattering from quantum impurities

TL;DR

This paper investigates the energy dependence of inelastic scattering from quantum impurities using a non-perturbative framework, analyzing various models including the two-channel Kondo and Anderson models, and exploring Fermi liquid versus non-Fermi liquid behaviors.

Contribution

It provides a detailed analysis of inelastic scattering and the energy dependence of the S-matrix for multiple quantum impurity models, highlighting differences between Fermi liquid and non-Fermi liquid regimes.

Findings

Half of the scattering remains inelastic at the Fermi energy in the two-channel Kondo model.

The study reveals a crossover between non-Fermi liquid and Fermi liquid regimes due to channel anisotropy.

The paper presents a path integral approach linking the T-matrix to local correlation functions.

Abstract

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.