Electron–Electron Scattering in Dense Plasma Transport: Why it Matters, Why it is Difficult, and What We Can Do About it Today

In the theory of plasma electron transport coefficients, a long-standing problem is a general and accurate account of electron–electron scattering effects. Historically, plasma kinetic theory has been the tool of choice to understand and quantify these effects. This line of research furnished valuable analytic results for classical and degenerate plasmas alike; however, they only hold for conditions of weak coupling and complete ionization. Over the past two decades, two promising and thus far complementary tracks have been developed. One is large-scale density functional theory (DFT)-based simulations with a Kubo–Greenwood treatment of electron transport. The other is advances in kinetic theory to treat non-ideal conditions, including generalized linear response approaches as well as mean-force kinetic theory. The successes and shortcomings of each approach will be summarized, with special attention paid to the fundamental and practical challenges that arise in trying to capture electron–electron scattering. Promising avenues for development on each track will be discussed, as well as prospects for combining DFT simulations and quantum kinetic theory for a high-fidelity model electron–electron scattering relevant to nonlocal transport effects.