Improved variational solutions of the Boltzmann-Ziman transport equation. Application to electronic transport in dense plasmas

Abstract
We study inelastic electron-ion scattering contributions to the thermoelectronic transport coefficients in dense plasmas which consist of a strongly coupled ionic component embedded in a highly degenerated electron jellium. When the electron component is taken as fully non-responding and when the ionic component contains solely one ion species of valence Z, these fluids can be modelled by the well-known one component plasma. Electronic transport coefficients, namely the electrical conductivity, the Lorentz number and the thermopower are deduced from improved variational solutions of the Boltzmann-Ziman transport equation detailed in this work. The latter are derived from a renormalized set of standard trial functions, taken as monomials in the electron energy. The renormalization is performed with the relaxation time pertaining to the exact solution of the BZ equation derived in the elastic case. We show that when restricted to the first two monomials, the variational solutions built in this way are strictly equivalent to their exact counterparts at any degeneracy. This new set of trial functions greatly modify the expression for the thermopower for which a new expression is proposed and next evaluated in the case of the dense hydrogen plasma.