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Dielectric function beyond RPA: kinetic theory vs. linear response theory

Calculating the frequency dependent dielectric function for strongly coupled plasmas, the relations within kinetic theory and linear response theory are derived and discussed in comparison. In this context, we proof the Kohler variational principle for arbitrary frequencies. It can be shown to be a special case of the Zubarev method for the construction of a non-equilibrium statistical operator from the principle of the extremum of entropy. Within kinetic theory, the commonly used energy dependent relaxation time approach is strictly valid only for the Lorentz plasma in the static case. It is compared with the result from linear response theory that includes electron-electron interactions and applies for arbitrary frequencies, including bremsstrahlung emission. It is shown how a general approach to linear response encompasses the different approximations and opens options for systematic improvements.