Non-adiabatic time-dependent density functional theory of the impurity resistivity of metals

We make use of the time-dependent density functional theory to derive a new formally exact expression for the dc resistivity of metals with impurities. This expression takes fully into account the dynamics of electron-electron interactions. Correction to the conventional $T$-matrix (phase-shifts) theory is treated within hydrodynamics of inhomogeneous viscous electron liquid. As a first application, we present calculations of the residual resistivity of aluminum as a function of the atomic number of the impurities. We show that the inclusion of many-body corrections considerably improves the agreement between theory and experiment.