Theory of inelastic scattering from magnetic impurities

Abstract

We use the numerical renormalization group method tocalculate the single particle matrix elements $\mathcal{T}$ of the many body $T$-matrix of the conduction electrons scattered by a magnetic impurity at T=0 temperature. Since $\mathcal{T}$ determines both the total and the elastic, spin-diagonal scattering cross sections, we are able to compute the full energy-, spin- and magnetic field dependence of the inelastic scattering cross section, ${\sigma }_{\mathrm{inel}}(\omega )$. We find an almost linear frequency dependence of ${\sigma }_{\mathrm{inel}}(\omega )$ below the Kondo temperature, $T_K$, which crosses over to a $\sim {\omega }^2$ behavior only at extremely low energies. Our method can be generalized to other quantum impurity models.

4 pages

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