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

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