Equation of state for weakly coupled quantum plasmas

Quantum theory for the dynamic structure factor in correlated two-component systems in nonequilibrium: Application to x-ray scattering

We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems.

Ab Initio Quantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

We perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with the linear response theory, we are able to remove finite-size errors from the potential energy over the substantial parts of the warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)]. Extensive new QMC results for up to N=1000 electrons enable us to compute the potential energy V and the exchange-correlation free energy F_{xc} of the macroscopic electron gas with an unprecedented accuracy of |ΔV|/|V|,|ΔF_{xc}|/|F|_{xc}∼10^{-3}. A comparison of our new data to the recent parametrization of F_{xc} by Karasiev et al. [Phys. Rev. Lett. 112, 076403 (2014)] reveals significant deviations to the latter.

Accurate Exchange-Correlation Energies for the Warm Dense Electron Gas

The density matrix quantum Monte Carlo (DMQMC) method is used to sample exact-on-average N-body density matrices for uniform electron gas systems of up to 10^{124} matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the k-space configuration path-integral formalism disagree by up to ∼10% at certain reduced temperatures T/T_{F}≤0.5 and densities r_{s}≤1. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that the DMQMC method can calculate free energies directly and present exact free energies for T/T_{F}≥1 and r_{s}≤2.

Ab Initio Thermodynamic Results for the Degenerate Electron Gas at Finite Temperature

The uniform electron gas at finite temperature is of key relevance for many applications in dense plasmas, warm dense matter, laser excited solids, and much more. Accurate thermodynamic data for the uniform electron gas are an essential ingredient for many-body theories, in particular, density-functional theory. Recently, first-principles restricted path integral Monte Carlo results became available, which, however, had to be restricted to moderate degeneracy, i.e., low to moderate densities with r_{s}=r[over ¯]/a_{B}≳1. Here we present novel first-principles configuration path integral Monte Carlo results for electrons for r_{s}≤4. We also present quantum statistical data within the e^{4} approximation that are in good agreement with the simulations at small to moderate r_{s}.

Effective potentials of interactions and thermodynamic properties of a nonideal two-temperature dense plasma

In this article a dense nonideal, nonisothermal plasma is considered. New effective screened interaction potentials taking into account quantum-mechanical diffraction and symmetry effects have been obtained. The effective potential of the ion-ion interaction in plasmas with a strongly coupled ion subsystem and semiclassical electron subsystem is presented. Based on the obtained effective potentials the analytical expressions for internal energy and the pressure of the considered plasma were obtained.

Cluster virial expansion of the equation of state for hydrogen plasma with e-H(2) contributions

The equation of state of partially ionized hydrogen plasma is considered with special focus on the contribution of the e-H(2) interaction. Traditional semiempirical concepts such as the excluded volume are improved using microscopic approaches to treat the e-H(2) problem. Within a cluster virial expansion, the Beth-Uhlenbeck formula is applied to infer the contribution of bound and scattering states to the temperature-dependent second virial coefficient. The scattering states are calculated using the phase expansion method for the polarization interaction that incorporates experimental data for the e-H(2) scattering cross section. We present results for the scattering phase shifts, differential scattering cross sections, and the second virial coefficient due to the e-H(2) interaction. The influence of this interaction on the composition of the partially ionized hydrogen plasma is confined to the parameter range where both the H(2) and the free-electron components are abundant.

Measurement of the adiabatic index in be compressed by counterpropagating shocks

We report on the first direct measurement of the adiabatic index γ through x-ray Thomson scattering from shock-compressed beryllium. 9 keV x-ray photons probe the bulk properties of matter during the collision of two counterpropagating shocks. This novel experimental technique determines γ by using only the measured mass densities and vanishing particle velocity at the point of shock collision to close the Rankine-Hugoniot equations. We find γ>5/3 at 3× compression, clearly different from ideal gas behavior. At 6× compression, γ shows the convergence to the ideal gas limit, in agreement with linear scaling laws.

Energy relaxation in dense, strongly coupled two-temperature plasmas

A quantum kinetic approach for the energy relaxation in strongly coupled plasmas with different electron and ion temperatures is presented. Based on the density operator formalism, we derive a balance equation for the energies of electrons and ions connecting kinetic, correlation, and exchange energies with a quite general expression for the electron-ion energy-transfer rate. The latter is given in terms of the correlation function of density fluctuations which allows for a derivation of increasingly realistic approximation schemes including a coupled-mode expression. The equilibration of the contributions of the total energy including the species temperatures in dense hydrogen and beryllium relevant for inertial confinement fusion is investigated as an example.

Single-particle spectral function for the classical one-component plasma

The spectral function for an electron one-component plasma is calculated self-consistently using the GW;{(0)} approximation for the single-particle self-energy. In this way, correlation effects that go beyond the mean-field description of the plasma are contained, i.e., the collisional damping of single-particle states, the dynamical screening of the interaction, and the appearance of collective plasma modes. Second, a nonperturbative analytic solution for the on-shell GW;{(0)} self-energy as a function of momentum is presented. It reproduces the numerical data for the spectral function with a relative error of less than 10% in the regime where the Debye screening parameter is smaller than the inverse Bohr radius, kappa<1a_{B};{-1} . In the limit of low density, the nonperturbative self-energy behaves as n;{14} , whereas a perturbation expansion leads to the unphysical result of a density-independent self-energy [Fennel and Wilfer, Ann. Phys. (Leipzig) 32, 265 (1974)]. The derived expression will greatly facilitate the calculation of observables in correlated plasmas (transport properties, equation of state) that need the spectral function as an input quantity. This is demonstrated for the shift of the chemical potential, which is computed from the analytical formulas and compared to the GW;{(0)} result. At a plasma temperature of 100eV and densities below 10;{21}cm;{-3} , the two approaches deviate by less than 10% from each other.

Structure of strongly coupled multicomponent plasmas

We investigate the short-range structure in strongly coupled fluidlike plasmas using the hypernetted chain approach generalized to multicomponent systems. Good agreement with numerical simulations validates this method for the parameters considered. We found a strong mutual impact on the spatial arrangement for systems with multiple ion species which is most clearly pronounced in the static structure factor. Quantum pseudopotentials were used to mimic diffraction and exchange effects in dense electron-ion systems. We demonstrate that the different kinds of pseudopotentials proposed lead to large differences in both the pair distributions and structure factors. Large discrepancies were also found in the predicted ion feature of the x-ray scattering signal, illustrating the need for comparison with full quantum calculations or experimental verification.