A quantum kinetic theory of the linear response to an electric field is provided from a controlled expansion of the Keldysh theory at leading order, for a multiband electron system with weak scalar disorder. The response is uniquely partitioned into intraband distribution functions and interband quantum coherences. A new explicit formula is provided for the latter, outlining their true nature as local dependent quantities, for which the mesoscopic gradients of the former are uncovered as a source term, opening a new research area. The precise connection with the Kubo formula in the ladder approximation is established. A pedagogical application to spin-orbit torque theory in the two-dimensional electron gas demonstrates the striking efficiency of the quantum kinetic approach. Some important implications for the theory of orbital transport are also briefly discussed.

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• Quantum transport
• Topological materials
• Nonequilibrium Green's function