Electrical conductivities for hot, dense hydrogen

Continuous Kubo-Greenwood formula: Theory and numerical implementation

In this paper, we present the so-called continuous Kubo-Greenwood formula intended for the numerical calculation of the dynamic Onsager coefficients and, in particular, the real part of dynamic electrical conductivity. In contrast to the usual Kubo-Greenwood formula, which contains the summation over a discrete set of transitions between electron energy levels, the continuous one is formulated as an integral over the whole energy range. This integral includes the continuous functions: the smoothed squares of matrix elements, D(ɛ,ɛ+ℏω), the densities of state, g(ɛ)g(ɛ+ℏω), and the difference of the Fermi weights, [f(ɛ)-f(ɛ+ℏω)]/(ℏω). The function D(ɛ,ɛ+ℏω) is obtained via the specially developed smoothing procedure. From the theoretical point of view, the continuous formula is an alternative to the usual one. Both can be used to calculate matter properties and produce close results. However, the continuous formula includes the smooth functions that can be plotted and examined. Thus, we can analyze the contributions of various parts of the electron spectrum to the obtained properties. The possibility of such analysis is the main advantage of the continuous formula. The continuous Kubo-Greenwood formula is implemented in the parallel code cubogram. Using the code we demonstrate the influence of technical parameters on the simulation results for liquid aluminum. We also analyze various methods of matrix elements computation and their effect on dynamic electrical conductivity.

Equations of state, transport properties, and compositions of argon plasma: combination of self-consistent fluid variation theory and linear response theory

A consistent theoretical model that can be applied in a wide range of densities and temperatures is necessary for understanding the variation of a material's properties during compression and heating. Taking argon as an example, we show that the combination of self-consistent fluid variational theory and linear response theory is a promising route for studying warm dense matter. Following this route, the compositions, equations of state, and transport properties of argon plasma are calculated in a wide range of densities (0.001-20 g/cm(3)) and temperatures (5-100 kK). The obtained equations of state and electrical conductivities are found in good agreement with available experimental data. The plasma phase transition of argon is observed at temperatures below 30 kK and density about 2-6g/cm(3). The minimum density for the metallization of argon is found to be about 5.8 g/cm(3), occurring at 30-40 kK. The effects of many-particle correlations and dynamic screening on the electrical conductivity are also discussed through the effective potentials.

Equation of state measurements of warm dense carbon using laser-driven shock and release technique

We present a new approach to equation of state experiments that utilizes a laser-driven shock and release technique combined with spatially resolved x-ray Thomson scattering, radiography, velocity interferometry, and optical pyrometry to obtain independent measurements of pressure, density, and temperature for carbon at warm dense matter conditions. The uniqueness of this approach relies on using a laser to create very high initial pressures to enable a very deep release when the shock moves into a low-density pressure standard. This results in material at near normal solid density and temperatures around 10 eV. The spatially resolved Thomson scattering measurements facilitate a temperature determination of the released material by isolating the scattering signal from a specific region in the target. Our results are consistent with quantum molecular dynamics calculations for carbon at these conditions and are compared to several equation of state models.

Pair-distribution functions of two-temperature two-mass systems: comparison of molecular dynamics, classical-map hypernetted chain, quantum Monte Carlo, and Kohn-Sham calculations for dense hydrogen

Two-temperature, two-mass quasiequilibrium plasmas may occur in electron-ion plasmas, nuclear-matter, as well as in electron-hole condensed-matter systems. Dense two-temperature hydrogen plasmas straddle the difficult partially degenerate regime of electron densities and temperatures which are important in astrophysics, in inertial-confinement fusion research, and other areas of warm dense-matter physics. Results from quantum Monte Carlo (QMC) are used to benchmark the procedures used in classical molecular-dynamics simulations and hypernetted chain (HNC) and classical-map HNC (CHNC) methods to derive electron-electron and electron-proton pair-distribution functions. Where QMC is not available, we used Kohn-Sham results as the reference calculation. Then, nonequilibrium molecular dynamics for two-temperature, two-mass plasmas are used to obtain pair distribution functions without specifying the interspecies cross temperature. Using these results, the correct HNC and CHNC procedures for the evaluation of pair-distribution functions in two-temperature two-mass two-component charged fluids are established and results for a mass ratio of 1:5, typical of electron-hole fluids, are presented.

Static and dynamic conductivity of warm dense matter within a density-functional approach: application to aluminum and gold

The conductivity sigma(omega) of dense Al and Au plasmas is considered where all the needed inputs are obtained from density-functional theory (DFT). These calculations involve a self-consistent determination of (i) the equation of state and the ionization balance, (ii) evaluation of the ion-ion and ion-electron pair-distribution functions, (iii) determination of the scattering amplitudes, and finally the conductivity. We present results for Al and Au for compressions 0.1-2.0, and in the temperature range T=0.1-10 eV. Excellent agreement with recent first-principles calculations using multi-ion density-functional molecular dynamics is obtained where the data fields overlap. We review first-principles approaches to the optical conductivity, including many-body perturbation theory, molecular-dynamics evaluations, and simplified time-dependent DFT. The modification to the Drude conductivity in the presence of shallow bound states in typical Al plasmas is examined and numerical results are given at the level of the Fermi Golden Rule and an approximate time-dependent DFT.

Simulations of fluid hydrogen: comparison of a dissociation model with tight-binding molecular dynamics

We compare the results of two complementary approaches, tight-binding molecular-dynamics simulations and a dissociation model, for determining the characteristics of dense, fluid hydrogen at pressures extending to megabars and temperatures to 10 000 K. Two tight-binding models were examined: one parametrization emphasized crystalline, molecular, and fluid properties, the other focused more on the intricate molecular interactions involving up to four hydrogen atoms. The two tight-binding cases and the dissociation model agree reasonably well for a variety of properties, including the equation of state, dissociation degree, and proton pair-correlation functions. In simulations of recently reported laser-driven shock experiments, the tight-binding and dissociative models predict different maximum compressions of four and five, respectively. We discuss the sensitivities of the models as well as give estimates for the region of validity of the chemical picture (dissociation model) and the accuracy of the dynamical picture (tight-binding simulations) in cases where molecular hydrogen still dominates the physical behavior.