In a recent Letter [T.~Dornheim \emph{et al.}, Phys.~Rev.~Lett.~\textbf{125}, 085001 (2020)], we have presented the first \emph{ab initio} results for the nonlinear density response of electrons in the warm dense matter regime. In the present work, we extend these efforts by carrying out extensive new path integral Monte Carlo (PIMC) simulations of a \emph{ferromagnetic} electron gas that is subject to an external harmonic perturbation. This allows us to unambiguously quantify the impact of spin-effects on the nonlinear density response of the warm dense electron gas. In addition to their utility for the description of warm dense matter in an external magnetic field, our results further advance our current understanding of the uniform electron gas as a fundamental model system, which is important in its own right.
We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) results for the spin-resolved density response of the uniform electron gas (UEG) at warm dense matter conditions. This allows us to unambiguously assess the accuracy of previous theoretical approximations, thereby providing valuable new insights for the future development of dielectric schemes. From a physical perspective, we observe a nontrivial manifestation of an effective electron--electron attraction that emerges in the spin-offdiagonal static density response function at strong coupling, $r_s\gtrsim5$. All PIMC re…
The study of warm dense matter, widely existing in nature and laboratories, is challenging due to the interplay of quantum and classical fluctuations. We develop a variational diagrammatic Monte Carlo method and determine the exchange-correlation kernel $K_{\rm XC}(q;T)$ of a warm dense electron gas for a broad range of temperature $T$ and momentum $q$. We observe several interesting physics, including the $T$-dependent evolution of the hump structure and the large-$q$ tail and the emergence of a scaling relation. Particularly, by deriving an analytical form for $q \to \infty$, we obtain large…
Warm dense matter (WDM) is an exotic state on the border between condensed matter and dense plasmas. Important occurrences of WDM include dense astrophysical objects, matter in the core of our Earth, as well as matter produced in strong compression experiments. As of late, x-ray Thomson scattering has become an advanced tool to diagnose WDM. The interpretation of the data requires model input for the dynamic structure factor $S(q,ω)$ and the plasmon dispersion $ω(q)$. Recently the first \textit{ab initio} results for $S(q,ω)$ of the homogeneous warm dense electron gas were obtained from path i…
We present first-principles calculations of the rate of energy exchanges between electrons and ions in nonequilibrium warm dense plasmas, liquid metals and hot solids, a fundamental property for which various models offer diverging predictions. To this end, a Kubo relation for the electron-ion coupling parameter is introduced, which includes self-consistently the quantum, thermal, non-linear and strong coupling effects that coexist in materials at the confluence of solids and plasmas. Most importantly, like other Kubo relations widely used for calculating electronic conductivities, the express…
A new variational principle for optimizing thermal density matrices is introduced. As a first application, the variational many body density matrix is written as a determinant of one body density matrices, which are approximated by Gaussians with the mean, width and amplitude as variational parameters. The method is illustrated for the particle in an external field problem, the hydrogen molecule and dense hydrogen where the molecular, the dissociated and the plasma regime are described. Structural and thermodynamic properties (energy, equation of state and shock Hugoniot) are presented.
The group velocity of a light pulse in photonic band gap material could considerably deviate from the speed of light in vacuum. Different speeds of a forward stoke and a pump pulse would enable the Raman compression in metals or the warm dense matter. A small window of the parameter regime, where the compression is feasible via the forward Raman scattering, is identified.
We predict the emergence of novel collective electronic excitations in warm dense matter with an inhomogeneous electronic structure based on first-principles calculations. The emerging modes are controlled by the imposed perturbation amplitude. They include satellite signals around the standard plasmon feature, transformation of plasmons to optical modes, and double-plasmon modes. Most importantly, these modes exhibit a pronounced dependence on the temperature. This makes them potentially invaluable for the diagnostics of plasma parameters in the warm dense matter regime. We demonstrate that t…
A precise calculation that translates shifts of X-ray K-absorption edges to variations of thermodynamic properties allows quantitative characterization of interior thermodynamic properties of warm dense plasmas by X-ray absorption techniques, which provides essential information for inertial confinement fusion and other astrophysical applications. We show that this interpretation can be achieved through an improved first-principles method. Our calculation shows that the shift of K-edges exhibits selective sensitivity to thermal parameters and thus would be a suitable temperature index to warm …
The decays of the Langmuir waves in dense plasmas are computed using the dielectric function theory widely used in the solid state physics. Four cases are considered: a classical plasma, a Maxwellian plasma, a degenerate quantum plasma, and a partially degenerate plasma. The result is considerably different from the conventional Landau damping theory.
We study the thermophysical properties of warm dense hydrogen using quantum molecular dynamics simulations. New results are presented for the pair distribution functions, the equation of state, the Hugoniot curve, and the reflectivity. We compare with available experimental data and predictions of the chemical picture. Especially, we discuss the nonmetal-to-metal transition which occurs at about 40 GPa in the dense fluid.
Warm dense matter is one of the most active frontiers in plasma physics due to its relevance for dense astrophysical objects as well as for novel laboratory experiments in which matter is being strongly compressed e.g. by high-power lasers. Its description is theoretically very challenging as it contains correlated quantum electrons at finite temperature---a system that cannot be accurately modeled by standard analytical or ground state approaches. Recently several breakthroughs have been achieved in the field of fermionic quantum Monte Carlo simulations. First, it was shown that exact simulat…
Understanding many processes, e.g. fusion experiments, planetary interiors and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter (WDM) and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly-free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive \emph{ab initio} atomistic computation, typically based on quantum mechanical Kohn-Sham Density Functional Theory (KS-DFT). However, cubic computational scaling with temperature and system size proh…
Wave packet molecular dynamics (WPMD) has recently received a lot of attention as a computationally fast tool to study dynamical processes in warm dense matter beyond the Born-Oppenheimer approximation. These techniques, typically, employ many approximations to achieve computational efficiency while implementing semi-empirical scaling parameters to retain accuracy. We investigate three of the main approximations ubiquitous to WPMD: a restricted basis set, approximations to exchange, and the lack of correlation. We examine each of these approximations in atomic and molecular hydrogen in additio…
The screening of a test charge by partially degenerate non-ideal free electrons at conditions related to warm dense matter and dense plasmas is investigated using linear response theory and the local field correction based on ab inito Quantum Monte-Carlo simulations data. The analysis of the obtained results is performed by comparing to the random phase approximation and the Singwi-Tosi-Land-Sjölander approximation. The applicability of the long-wavelength approximation for the description of screening is investigated. The impact of electronic exchange-correlations effects on structural proper…
Accurate modeling of the electronic structure of warm dense matter is a challenging problem whose solution would allow a better understanding of material properties like equation of state, opacity, and conductivity, with resulting applications from astrophysics to fusion energy research. Here we explore the real-space Green's function method as a technique for solving the Kohn-Sham density functional theory equations under warm dense matter conditions. We find the method to be tractable and accurate throughout the density and temperature range of interest, in contrast to other approaches. Good…
We demonstrate the abilities of elastic x-ray scattering to yield information on dense matter with multiple ion species and on the microscopic mixing in dense materials. Based on partial structure factors from ab initio simulations, a novel approach for the elastic scattering feature is applied to dense hydrogen-beryllium and hydrogen-helium mixtures. The scattering signal differs significantly between single species, real microscopic mixtures, and two separate fluids in the scattering volume.
Warm dense matter is a highly active research area both at the frontier and interface of material science and plasma physics. We assess the performance of commonly used exchange-correlation (XC) approximation (LDA, PBE, PBEsol, and AM05) in the spin-polarized inhomogeneous electron gas under warm dense conditions based on exact path-integral quantum Monte-Carlo calculations. This extends our recent analysis on the relevance of inhomogeneities in the spin-unpolarized warm dense electron gas [Z.~Moldabekov et al., J. Chem. Phys. 155, 124116 (2021)]. We demonstrate that the predictive accuracy of…
Warm dense matter is difficult to generate since it corresponds to a state of matter which pressure is order of magnitude larger than can be handled by natural materials. A diamond anvil can be used to pressurize matter up to one Gbar, this matter is at high density but at room temperature. High power lasers and heavy ion beams can generate warm dense matter but they cannot confine it long enough to allow measurements of quasi-static transport coefficients such as viscosity or heat conduction. We present here a third method to generate warm dense matter. It uses a pulsed-power driver which cur…
We have calculated the equation of states, the viscosity and self-diffusion coefficients, and electronic transport coefficients of beryllium in the warm dense regime for densities from 4.0 to 6.0 g/cm$^{3}$ and temperatures from 1.0 to 10.0 eV by using quantum molecular dynamics simulations. The principal Hugoniot is accordant with underground nuclear explosive and high power laser experimental results up to $\sim$ 20 Mbar. The calculated viscosity and self-diffusion coefficients are compared with the one-component plasma model, using effective charges given by the average-atom model. The Stok…
The rate of photon absorption in warm dense matter (WDM) induced by free-free electron-ion collisions is derived from Sommerfeld's cross-section for non-relativistic bremsstrahlung emission, making use of detailed balance relations. Warm dense matter is treated as a metal-like state in the approximation of a uniform degenerate electron gas and a uniform ion background. Total absorption rates are averaged over the electron Fermi distribution. A closed expression is obtained for the absorption rate, depending on temperature, density, and photon energy, that scales with ion charge Z. It is evalua…
The Ziman formulation of electrical conductivity is tested in warm and hot dense matter using the pseudo-atom molecular dynamics method. Several implementation options that have been widely used in the literature are systematically tested through a comparison to accurate but expensive Kohn-Sham density functional theory molecular dynamics (KS-DFT-MD) calculations. The comparison is made for several elements and mixtures and for a wide range of temperatures and densities, and reveals a preferred method that generally gives very good agreement with the KSDFT-MD results, but at a fraction of the …
Accurate equations of state (EOS) and plasma transport properties are essential for numerical simulations of warm dense matter encountered in many high-energy-density situations. Molecular dynamics (MD) is a simulation method that generates EOS and transport data using an externally provided potential to dynamically evolve the particles without further reference to the electrons. To minimize computational cost, pair potentials needed in MD may be obtained from the neutral-pseudoatom (NPA) approach, a form of single-ion density functional theory (DFT), where many-ion effects are included via io…
The energy band structures caused by self-energy shifting that results in bound energy levels broadening and merging in warm dense aluminum and beryllium are observed. An energy band theory for warm dense matter (WDM) is proposed and a new code based on the energy band theory is developed to improve the traditional density functional method. Massive data of the equation of state and transport coefficients for WDM in medium and low Z have been simulated. The transition from fully degenerate to partially degenerate (related to WDM) and finally to non-degenerate state is investigated using the Lo…
Warm dense matter (WDM) -- an exotic state of highly compressed matter -- has attracted high interest in recent years in astrophysics and for dense laboratory systems. At the same time, this state is extremely difficult to treat theoretically. This is due to the simultaneous appearance of quantum degeneracy, Coulomb correlations and thermal effects, as well as the overlap of plasma and condensed phases. Recent breakthroughs are due to the successful application of density functional theory (DFT) methods which, however, often lack the necessary accuracy and predictive capability for WDM applica…
We report ab initio calculations of the valence electron momentum distribution function n(p) and dynamic structure factor for warm dense Be at Mbar pressures. We observe an unexpected, strong reshaping of the Compton profile upon increasing density, even well before any significant core-wavefunction overlap or electride behavior occurs. We propose that this nonperturbative effect, which is due to a growing influence on n(p) of the orthogonalization of valence and core electron wave- functions with increasing density, is observable by inelastic x-ray scattering at x-ray free-electron lasers and…
In a recent letter [\textit{Phys.~Rev.~Lett.}~\textbf{125}, 085001 (2020)], Dornheim \textit{et al.}~have presented the first \textit{ab initio} path integral Monte Carlo (PIMC) results for the nonlinear electronic density response at warm dense matter (WDM) conditions. In the present work, we extend these considerations by exploring the relation between the nonlinear response and three-/four-body correlation functions from many-body theory. In particular, this connection directly implies a comparably increased sensitivity of the nonlinear response to electronic exchange-correlation (XC) effec…
In a recent Letter [T.~Dornheim \textit{et al.}, Phys. Rev. Lett. \textbf{117}, 156403 (2016)], we presented the first \textit{ab initio} quantum Monte-Carlo (QMC) results of the warm dense electron gas in the thermodynamic limit. However, a complete parametrization of the exchange-correlation free energy with respect to density, temperature, and spin polarization remained out of reach due to the absence of (i) accurate QMC results below $θ=k_\text{B}T/E_\text{F}=0.5$ and (ii) of QMC results for spin polarizations different from the paramagnetic case. Here we overcome both remaining limitation…
The controversy with respect to the role of electron-electron collisions in the dynamic conductivity of dense plasmas is resolved. In particular, the dc conductivity is analyzed in the low-density, non-degenerate limit where the Spitzer theory is valid and electron-electron collisions lead to the well-known reduction of the result for a Lorentz plasma. With increasing degeneracy, the contribution of electron-electron collisions to the dc conductivity is decreasing and can be neglected for the liquid metal domain where the Ziman-Faber theory is applicable. We show how electron-electron collisio…
In the present paper we propose the use of desnity matrix formalism for the calculation of the atomic spectroscopic properties of autoionizing states in dense plasmas, i.e. warm dense matter and strongly coupled plasmas. This is motivated by the importance of taking into account the effect of the electric microfield generated by the plasma charge constituents in the calculation of the atomic populations of autoionizing states. For autoionizing states, electron densities justifying the statistical approach exceed solid density bringing serious doubts to the statistical approach even in dense pl…
Fundamental properties of warm dense matter are described by the dielectric function, which gives access to the frequency-dependent electrical conductivity, absorption, emission and scattering of radiation, charged particles stopping and further macroscopic properties. Different approaches to the dielectric function and the related dynamical collision frequency are compared in a wide frequency range. The high-frequency limit describing inverse bremsstrahlung and the low-frequency limit of the dc conductivity are considered. Sum rules and Kramers-Kronig relation are checked for the generalized …
The dynamic electron-ion collisions play an important rolein determining the static and transport properties of warmdense matter (WDM). Electron force field (eFF) method is applied to study the ionic transport properties of warm densehydrogen. Compared with the results from quantum moleculardynamics and orbital-free molecular dynamics, the ionicdiffusions are largely reduced by involving the dynamic collisions of electrons and ions. This physics is verified by quantum Langevin molecular dynamics (QLMD) simulations, which includes electron-ion collisions induced friction(EI-CIF) into the dynami…
The decay of the Langmuir waves in dense plasmas is not accurately predicted by the prevalent Landau damping theory. A dielectric function theory is introduced, predicting much higher damping than the Landau damping theory. This strong damping is in better agreement with the experimentally observed data in metals. It is shown that the strong plasmon decay leads to the existence of a parameter regime where the backward Raman scattering is unstable while the forward Raman scattering is stable. This regime may be used to create intense x-ray pulses, by means of the the backward Raman compression.…
Warm dense matter (WMD) describes an intermediate phase, between condensed matter and classical plasmas, found in natural and man-made systems. In a laboratory setting, WDM needs to be created dynamically. It is typically laser or pulse-power generated and can be difficult to characterize experimentally. Measuring the energy loss of high energy ions, caused by a WDM target, is both a promising diagnostic and of fundamental importance to inertial confinement fusion research. However, electron coupling, degeneracy, and quantum effects limit the accuracy of easily calculable kinetic models for st…
Photonic band gaps for the soft x-rays, formed in the periodic structures of solids or dense plasmas, are theoretically investigated. Optical manipulation mechanisms for the soft x-rays, which are based on these band gaps, are computationally demonstrated. The reflection and amplification of the soft x-rays, and the compression and stretching of chirped soft x-ray pulses are discussed. A scheme for lasing with atoms with two energy levels, utilizing the band gap, is also studied.
Ionization and temperature measurements in warm dense copper using x-ray absorption spectroscopy
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Mechanical and Aerospace Engineering, University of California San Diego（加州大学圣地亚哥分校机械与航空航天工程系）；Laboratory for Laser Energetics, University of Rochester（罗切斯特大学激光能量学实验室）；Sandia National Laboratories（桑迪亚国家实验室）
Experimentally observed decay rate of the long wavelength Langmuir wave in metals and dense plasmas is orders of magnitude larger than the prediction of the prevalent Landau damping theory. The discrepancy is explored, and the existence of a regime where the forward Raman scattering is stable and the backward Raman scattering is unstable is examined. The amplification of an x-ray pulse in this regime, via the backward Raman compression, is computationally demonstrated, and the optimal pulse duration and intensity is estimated.
Informing spectral models for dense plasmas with K-edge absorption measurements of warm dense copper
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；University of California San Diego（加州大学圣地亚哥分校）；Laboratory for Laser Energetics, University of Rochester（罗切斯特大学激光能量学实验室）；Sandia National Laboratories（桑迪亚国家实验室）；University of Oxford（牛津大学）
Principal Hugoniot and K-shell X-ray absorption spectra of warm dense KCl are calculated using the first-principles molecular dynamics method. Evolution of electronic structures as well as the influence of the approximate description of ionization on pressure (caused by the underestimation of the energy gap between conduction bands and valence bands) in the first-principles method are illustrated by the calculation. Pressure ionization and thermal smearing are shown as the major factors to prevent the deviation of pressure from global accumulation along the Hugoniot. In addition, cancellation …
We perform \emph{ab initio} quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with linear response theory we are able to remove finite-size errors from the potential energy over the entire warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown \emph{et al.}~[PRL \textbf{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 a…
The study of matter under extreme densities and temperatures as they occur e.g. in astrophysical objects and nuclear fusion applications has emerged as one of the most active frontiers in physics, material science, and related disciplines. In this context, a key quantity is given by the dynamic structure factor $S(\mathbf{q},ω)$, which is probed in scattering experiments -- the most widely used method of diagnostics at these extreme conditions. In addition to its crucial importance for the study of warm dense matter, the modelling of such dynamic properties of correlated quantum many-body syst…
We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed ion configurations from density functional theory molecular dynamics (DFT-MD) simulations to solve the electronic problem for hydrogen under warm dense matter conditions [M.Böhme et. al. Phys.Rev.Lett.(in print)]. The problem of path collapse due to the Coulomb attraction is avoided by utilizing the pair approximation, which is compared against the simpler Kelbg pair-potential. We find very favourable convergence behaviour towards the former. Since we do not impose any nodal restrictions, our PIMC simulations are affl…
Megabar (1 Mbar = 100 GPa) laser shocks on precompressed samples allow reaching unprecedented high densities and moderately high 10000-100000K temperatures. We describe here a complete analysis framework for the velocimetry (VISAR) and pyrometry (SOP) data produced in these experiments. Since the precompression increases the initial density of both the sample of interest and the quartz reference for pressure-density, reflectivity and temperature measurements, we describe analytical corrections based on available experimental data on warm dense silica and density-functional-theory based molecul…
