Conductivity of Kondo-type systems in the presence of crystal fields

By starting with the expression for the conductivity of Kondo-type systems in the presence of crystal fields as calculated by the Kubo formalism, we derive the expression found from the Boltzmann equation. To rewrite the compact Kubo expression in the more cumbersome expression found in the semiclassical Boltzmann approach, we use a generalization of the optical theorem to finite-temperature propagators. Also, we calculate the conductivity through third order in the coupling constant J=$V^2$/$E_f$ and obtain agreement with previous results.