Perturbation Theoretic Calculation of Polaron Mobility

The low-temperature drift mobility of the polaron is calculated in perturbation theory with the aid of the Kubo formula. The result is μ=μ₀(1-α6), where μ₀ is the weak coupling mobility μ₀=(e2αωm)exp(ωkT). A comparison is made with the perturbation expansion of various intermediate coupling mobility theories. The expansion of Osaka, μ=μ₀(1-0.173α+⋯), agrees most closely with the exact perturbation expansion. It is concluded that the Osaka formula is probably the best in the intermediate coupling range α<6. It is explicitly shown to lowest nontrivial order in α that various quasiparticle concepts are valid, viz., that μ=eτm*, and that the electron density is a momentum integral over f(E(p)).