Here, linear response theory, the Kubo and Kubo-Luttinger equations, is introduced in quite a general context from which for independent particles, namely in the context of density functional theory, a Kubo equation is derived that applies to electric as well as optical transport. For both aspects (zero and finite frequencies) a Green’s function formulation in terms of multiple scattering is given. In particular, the importance of inherent boundary conditions and the concept of layer-resolved conductivities are discussed.

16.1 Linear response theory In the 1950s Kubo developed a method of evaluating the response of a quantum mechanical system to an external potential, in particular to an electric field [1]. To first order, known as linear response, this kind of response theory [2, 3] is applicable to electric as well as to optical transport. In the following the underlying theoretical approach is introduced and will then be cast into a multiple scattering formulation [4, 5, 6].