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

TL;DR

This paper compares kinetic theory and linear response theory for calculating the dielectric function in strongly coupled plasmas, demonstrating the validity of the Kohler variational principle and highlighting the advantages of linear response methods.

Contribution

It establishes the Kohler variational principle within the context of dielectric function calculations and compares kinetic and linear response theories, including electron-electron interactions.

Findings

Kohler variational principle proven for arbitrary frequencies

Energy-dependent relaxation time valid only for static Lorentz plasma

Linear response theory includes electron-electron interactions and applies at all frequencies

Abstract

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.