The equation of state for hydrogen at high densities

Vorberger, Jan; Gericke, Dirk O.; Kraeft, W. D.

doi:10.1016/j.hedp.2013.04.011

Cited by 21 publications

(33 citation statements)

References 75 publications

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“…The price to pay is that we have to avoid the regions where these species are dominant. With respect to accuracy the rather simple formulae given here may not compete with the recent successful approaches to dense plasmas based on numerical methods [52,53,54]. We are convinced however, that in particular to experimentalists, analytical approaches may always be quite useful in complementing numerical results.…”

Section: Discussionmentioning

confidence: 92%

“…Copyright line will be provided by the publisher 18Ebeling, Kraeft, and Röpke: On the quantum statistics of bound states within the Rutherford model of matter Comparison of the analytical theory for T = 20000 K (magenta) and T = 50000 K (green) to the results of a numerical code developed earlier within the chemical picture[21,22,24,51,53] (blue: T = 20000 K, red: T = 50000 K). We show the relation of the pressure to the classical ideal pressure of the ions nkBT .…”

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confidence: 99%

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On the quantum statistics of bound states within the Rutherford model of matter

2012

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The quantum statistical treatment of the Rutherford model is analyzed, considering matter as a system of point charges (electrons and nuclei). First, the solutions of different fundamental problems are discussed, such as the divergence of the partition function, elaborated by Herzfeld, Planck, Brillouin and Rompe. Beyond this analysis in the historical context, the modern state of art is presented and new results are given which explain why bound states according to a discrete part of the spectra occur only in a valley in the temperature-density plane. Based on the actual state of the quantum statistics of Coulomb systems, virial expansions within the canonical ensemble and the grand ensemble and combinations are derived. Furthermore, the transitions along isotherms are studied: (i) the formation of bound states occurring by increasing the density from low to moderate values, (ii) the disappearance of bound state effects at higher densities. Within the physical picture isotherms of pressure for hydrogen are calculated in a broad density region. It is shown that in the region between 20 000 K and 100 000 K and particle densities below 10 22 cm −3 the cross-over from full to partial ionization may be well described by the contributions of extended ring diagrams and ladder diagrams.

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Section: Discussionmentioning

confidence: 92%

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confidence: 99%

On the quantum statistics of bound states within the Rutherford model of matter

2012

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“…If the off-diagonal elements of the polarization functions are retained, as in Eqs. (55) and (56), the generalized screening cloud includes the bound-electron (ionic) form factor, the screening cloud of free electrons, and also in principle any bound-free transitions. The actual evaluation of the ion form factor or bound-free transitions in non-equilibrium depends on the ability to either solve the screened ladder for the polarization function or to incorporate solutions of the time-dependent Schrödinger equation into the present formalism.…”

Section: Decomposition Of the Dynamic Structure Factor In Non-equimentioning

confidence: 99%

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

Vorberger

Chapman

2018

Phys. Rev. E

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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.

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“…This allows for the construction of a true non-local XC functional, which is a promising approach to go beyond the ubiquitous gradient approximations [18,26] and thereby increase the predictive capabilities of DFT. Further applications of the LFCs for current warm dense matter (WDM, see below) research include the calculation of the dynamic structure factor [27][28][29][30] as it can be obtained with X-ray Thomson scattering from a variety of systems, energy transfer rates [31,32], the electrical and optical conductivity [33,34], and equation of state models of ionized plasmas [35][36][37]. Finally, we mention the construction of effective potentials both for WDM [38,39] and beyond [40,41].…”

Section: Introductionmentioning

confidence: 99%

Permutation-blocking path-integral Monte Carlo approach to the static density response of the warm dense electron gas

et al. 2017

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The static density response of the uniform electron gas is of fundamental importance for numerous applications. Here, we employ the recently developed ab initio permutation blocking path integral Monte Carlo (PB-PIMC) technique [T. Dornheim et al., New J. Phys. 17, 073017 (2015)] to carry out extensive simulations of the harmonically perturbed electron gas at warm dense matter conditions. In particular, we investigate in detail the validity of linear response theory and demonstrate that PB-PIMC allows to obtain highly accurate results for the static density response function and, thus, the static local field correction. A comparison with dielectric approximations to our new ab initio data reveals the need for an exact treatment of correlations. Finally, we consider a superposition of multiple perturbations and discuss the implications for the calculation of the static response function.

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The equation of state for hydrogen at high densities

Cited by 21 publications

References 75 publications

On the quantum statistics of bound states within the Rutherford model of matter

On the quantum statistics of bound states within the Rutherford model of matter

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

Permutation-blocking path-integral Monte Carlo approach to the static density response of the warm dense electron gas

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