Semiclassical approach to calculating the influence of local lattice   fluctuations on electronic properties of metals
  We propose a new semiclassical approach based on the dynamical mean field theory to treat the interactions of electrons with local lattice fluctuations. In this approach the classical (static) phonon modes are treated exactly whereas the quantum (dynamical) modes are expanded to second order and give rise to an effective semiclassical potential. We determine the limits of validity of the approximation, and demonstrate its usefulness by calculating the temperature dependent resistivity in the Fermi liquid to polaron crossover regime (leading to `saturation behavior') and also isotope effects on electronic properties including the spectral function, resistivity, and optical conductivity, problems beyond the scope of conventional diagrammatic perturbation theories. 
S. Blawid, A. Deppeler, A.J. Millis