One-body models for transport properties of valence fluctuators: Exact results

We consider various transport processes for (a) the resonant level lattice and (b) the dilute resonant level scattering of conduction electrons. These models, of possible relevance to valence fluctuators, consist of narrow resonant levels hybridizing with a broad conduction-band continuum. For case (a), hybridization results in strongly-energy-dependent effective masses in the vicinity of the resonance energy. However, these mass effects do not appear in the plasma frequency or the dc resistivity. Indeed, for normal conduction-electron impurity scattering, the weak-coupling memory function method, the exact Boltzmann-equation solution, and the exact Green’s-function solution (in the dilute limit) are shown to be in essential agreement. For normal electron-phonon scattering we show that the weak-coupling memory function approach treated correctly to second order in the electron-phonon coupling yields the Bloch-Grüneisen law despite the presence of large, energy-dependent effective masses. Moreover, application of nonconserving approximations which have previously yielded appealing fits to the resistivity of valence fluctuating ${\mathrm{CePd}}_3$ cannot account for the striking absorptivity of that material. Finally, we show for case (b) that the weak-coupling memory function approach yields resistivities in qualitative disagreement with the exact Boltzmann equation, although the zero-temperature ac conductivity agrees quite well in the dilute limit. We conclude that the weak-coupling memory function approach is ill suited for calculating transport properties in the presence of resonant scattering.