  The Feynman path-integral variational approach to the polaron
problem\cite{Feynman1955}, along with the associated FHIP linear-response
mobility theory\cite{Feynman1962}, provides a computationally amenable method
to predict the frequency-resolved temperature-dependent charge-carrier
mobility, and other experimental observables in polar semiconductors. We show
that the FHIP mobility theory predicts non-Drude transport behaviour, and shows
remarkably good agreement with the recent diagrammatic Monte-Carlo mobility
simulations of Mishchenko et al.\cite{Mishchenko2019} for the abstract
Fr\"ohlich Hamiltonian.
  We extend this method to multiple phonon modes in the Fr\"ohlich model
action. This enables a slightly better variational solution, as inferred from
the resulting energy. We carry forward this extra complexity into the mobility
theory, where it shows richer structure in the frequency and temperature
dependent mobility, due to the different phonon modes activating at different
energies.
  The method provides a computationally efficient and fully quantitative method
of predicting polaron mobility and response in real materials.
