Variational approach to the average-atom-in-jellium and superconfigurations-in-jellium models with all electrons treated quantum-mechanically
TL;DR: In this paper, the authors used a cluster expansion of the free energy expression from which they retained the sum of the zero and the first order terms of the first-order terms.
About: This article is published in High Energy Density Physics.The article was published on 2007-05-01. It has received 33 citations till now. The article focuses on the topics: Jellium & Ionization.
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TL;DR: In this article, the authors calculated electrical and thermal conductivities of warm and hot dense matter using two versions of the average-atom approach: Liberman's model and the neutral Wigner-Seitz-sphere model.
40 citations
TL;DR: In this article, a self-consistent joint description of free and weakly bound electron states in strongly coupled plasmas is presented and the existence of two problems is emphasized.
Abstract: A self-consistent joint description of free and weakly bound electron states in strongly coupled plasmas is presented. The existence of two problems is emphasized. The first one is a well-known restriction of the number of atomic excitedstates. Anotheroneisadescriptionofthesmoothcrossoverfrombound pair electron‐ion excited states to collective excitations of free electrons. The fluctuation approach is developed to study the spectrum domain intermediate between low-lying excited atoms and free electron continuous energy levels. The molecular dynamics method is applied to study the plasma model since the method is able to distinguish all kinds of fluctuations. The electron‐ ion interaction is described by the temperature-independent cut-off Coulomb potential. The diagnostics of pair electron‐ion fluctuations is developed. The concept of pair fluctuations elucidates the smooth vanishing of atomic states neartheionizationlimit. Theapproachsuggestedremovestheartificialbreakof the electron state density at the ionization limit: atomic state density divergent at the negative energy side and free electron state density starting from zero density at the positive energy side.
38 citations
TL;DR: The resulting EOS thus includes a quantum mechanical treatment of the electrons with a self-consistent model of the ionic structure, while remaining tractable at high temperatures, and shows remarkable thermodynamic consistency over a wide range of temperatures for aluminum.
Abstract: We present an approximation for calculating the equation of state (EOS) of warm and hot dense matter that is built on the previously published pseudoatom molecular dynamics (PAMD) model of dense plasmas [Starrett et al., Phys. Rev. E 91, 013104 (2015)PLEEE81539-375510.1103/PhysRevE.91.013104]. While the EOS calculation with PAMD was previously limited to orbital-free density functional theory (DFT), the new approximation presented here allows a Kohn-Sham DFT treatment of the electrons. The resulting EOS thus includes a quantum mechanical treatment of the electrons with a self-consistent model of the ionic structure, while remaining tractable at high temperatures. The method is validated by comparisons with pressures from ab initio simulations of Be, Al, Si, and Fe. The EOS in the Thomas-Fermi approximation shows remarkable thermodynamic consistency over a wide range of temperatures for aluminum. We calculate the principal Hugoniots of aluminum and silicon up to 500 eV. We find that the ionic structure of the plasma has a modest effect that peaks at temperatures of a few eV and that the features arising from the electronic structure agree well with ab initio simulations.
30 citations
TL;DR: The progress in the theoretical study of WDM is reviewed with state-of-the-art simulations, i.e. quantum Langevin molecular dynamics and first principles path integral molecular dynamics.
Abstract: The structural, thermodynamic and transport properties of warm dense matter (WDM) are crucial to the fields of astrophysics and planet science, as well as inertial confinement fusion. WDM refers to the states of matter in a regime of temperature and density between cold condensed matter and hot ideal plasmas, where the density is from near-solid up to ten times solid density, and the temperature between 0.1 and 100 eV. In the WDM regime, matter exhibits moderately or strongly coupled, partially degenerate properties. Therefore, the methods used to deal with condensed matter and isolated atoms need to be properly validated for WDM. It is therefore a big challenge to understand WDM within a unified theoretical description with reliable accuracy. Here, we review the progress in the theoretical study of WDM with state-of-the-art simulations, i.e. quantum Langevin molecular dynamics and first principles path integral molecular dynamics. The related applications for WDM are also included.
27 citations
TL;DR: In this article, a new Ehrenfest-type sum rule, originally proposed in the quantum VAAQP model, was proven in the case of the response of the TF atom with the Bloch hydrodynamics (TFB) and checked by numerical example.
20 citations
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TL;DR: In this article, a variational property of the ground-state energy of an electron gas in an external potential, derived by Hohenberg and Kohn, is extended to nonzero temperatures.
Abstract: A variational property of the ground-state energy of an electron gas in an external potential $v(\mathrm{r})$, derived by Hohenberg and Kohn, is extended to nonzero temperatures. It is first shown that in the grand canonical ensemble at a given temperature and chemical potential, no two $v(\mathrm{r})$ lead to the same equilibrium density. This fact enables one to define a functional of the density $F[n(\mathrm{r})]$ independent of $v(\mathrm{r})$, such that the quantity $\ensuremath{\Omega}=\ensuremath{\int}v(\mathrm{r})n(\mathrm{r})d\mathrm{r}+F[n(\mathrm{r})]$ is at a minimum and equal to the grand potential when $n(\mathrm{r})$ is the equilibrium density in the grand ensemble in the presence of $v(\mathrm{r})$.
2,117 citations
TL;DR: The Fermi-Thomas model has been used to derive the equation of state of matter at high pressures and at various temperatures as discussed by the authors, and the similarity transformations lead to the virial theorem and correlation of solutions for different Z values.
Abstract: The Fermi-Thomas model has been used to derive the equation of state of matter at high pressures and at various temperatures. Calculations have been carried out both without and with the exchange terms. Discussion of similarity transformations lead to the virial theorem and to correlation of solutions for different Z values.
640 citations
TL;DR: A method is presented for calculating the bound-bound emission from a local thermodynamic equilibrium plasma and it is shown that under certain plasma conditions the contributions of low-probability transitions can accumulate into an important component of the emission.
Abstract: A method is presented for calculating the bound-bound emission from a local thermodynamic equilibrium plasma. The total transition array of a specific single-electron transition, including all possible contributing configurations, is described by only a small number of super-transition-arrays (STA's). Exact analytic expressions are given for the first few moments of an STA. The method is shown to interpolate smoothly between the average-atom (AA) results and the detailed configuration accounting that underlies the unresolved transition array (UTA) method. Each STA is calculated in its own, optimized potential, and the model achieves rapid convergence in the number of STA's included. Comparisons of predicted STA spectra with the results of the AA and UTA methods are presented. It is shown that under certain plasma conditions the contributions of low-probability transitions can accumulate into an important component of the emission. In these cases, detailed configuration accounting is impractical. On the other hand, the detailed structure of the spectrum under such conditions is not described by the AA method. The application of the STA method to laser-produced plasma experiments is discussed.
319 citations