Theory of resistivity of metals

An expression for the resistivity in terms of a force-force correlation function is considered. It is shown from the standard Kubo current-current correlation function formula (1956) for the conductivity in the weak-scattering limit, that this expression for the resistivity is valid if evaluated not for the actual specimen but for a hypothetical system in which the specimen is immersed in an infinite bath of free or Bloch electrons. The author also shows how the expression can then be rewritten in terms of the scattering operator for the entire system of ions and exemplify this by obtaining (a) in the high-temperature limit, an expression previously proposed by Rousseau et al. (1972) and (b) at general temperatures, the Baym (1964) formula (which reduces to the Ziman formula (1964) for the resistivity of the liquid metal at high temperatures), thereby giving an exact definition of the relevant pseudopotential as the single-centre scattering matrix.