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Register a new userSelf-energy effects and energy band theory for warm dense matter
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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 Lorenz number varying with the degeneracy parameter, and the lower and upper parameter boundaries for WDM are achieved. It is shown that the pressure ionization results in the Wiedemann-Franz law no longer available for WDM.
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We investigate the energy loss characteristics of warm dense matter (WDM) and dense plasmas concentrating on the influence of electronic correlations. The basis for our analysis is a recently developed ab initio Quantum Monte-Carlo (QMC) based machine-learning representation of the static local field correction (LFC) [Dornheim et al., J. Chem. Phys. 151, 194104 (2019)], which provides an accurate description of the dynamical density response function of the electron gas at the considered parameters. We focus on the polarization-induced stopping power due to free electrons, the friction function, and the straggling rate. In addition, we compute the friction coefficient which constitutes a key quantity for the adequate Langevin dynamics simulation of ions. Considering typical experimental WDM parameters with partially degenerate electrons, we find that the friction coefficient is of the order of $gamma/omega_{pi}=0.01$, where $omega_{pi}$ is the ionic plasma frequency. This analysis is performed by comparing QMC based data to results from the random phase approximation (RPA), the Mermin dielectric function, and the Singwi-Tosi-Land-Sjolander (STLS) approximation. It is revealed that the widely used relaxation time approximation (Mermin dielectric function) has severe limitations regarding the description of the energy loss properties of correlated partially degenerate electrons. Moreover, by comparing QMC based data with the results obtained using STLS, we find that energy loss properties are not sensitive to the inaccuracy of the static LFC at large wave numbers $k/k_{F}>2$ (with $k_F$ being the usual Fermi wave number), but that a correct description of the static LFC at $k/k_{F}lesssim 1.5$ is important.
We present an emph{Effective Static Approximation} (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor $S(q,omega)$, the static structure factor $S(q)$, and the interaction energy $v$. The ESA combines the recent neural-net representation [textit{J. Chem. Phys.} textbf{151}, 194104 (2019)] of the temperature dependent LFC in the exact static limit with a consistent large wave-number limit obtained from Quantum Monte-Carlo data of the on-top pair distribution function $g(0)$. It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by re-evaluating the results of the recent {X-ray Thomson scattering experiment on aluminum} by Sperling textit{et al.}~[textit{Phys. Rev. Lett.} textbf{115}, 115001 (2015)]. We find that an accurate incorporation of electronic correlations {in terms of the ESA} leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like the Mermin approach or linear-response time-dependent density functional theory. Furthermore, the ESA scheme is particularly relevant for the development of advanced exchange-correlation functionals in density functional theory.
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 applications. The situation has changed with the availability of the first textit{ab initio} data for the exchange-correlation free energy of the warm dense uniform electron gas (UEG) that were obtained by quantum Monte Carlo (QMC) simulations, for recent reviews, see Dornheim textit{et al.}, Phys. Plasmas textbf{24}, 056303 (2017) and Phys. Rep. textbf{744}, 1-86 (2018). In the present article we review recent further progress in QMC simulations of the warm dense UEG: namely, textit{ab initio} results for the static local field correction $G(q)$ and for the dynamic structure factor $S(q,omega)$. These data are of key relevance for the comparison with x-ray scattering experiments at free electron laser facilities and for the improvement of theoretical models. In the second part of this paper we discuss simulations of WDM out of equilibrium. The theoretical approaches include Born-Oppenheimer molecular dynamics, quantum kinetic theory, time-dependent DFT and hydrodynamics. Here we analyze strengths and limitations of these methods and argue that progress in WDM simulations will require a suitable combination of all methods. A particular role might be played by quantum hydrodynamics, and we concentrate on problems, recent progress, and possible improvements of this method.
A scheme for analyzing Thomson scattering of x-rays by warm dense matter, based on the average-atom model, is developed. Emphasis is given to x-ray scattering by bound electrons. Contributions to the scattered x-ray spectrum from elastic scattering by electrons moving with the ions and from inelastic scattering by free and bound electrons are evaluated using parameters (chemical potential, average ionic charge, free electron density, bound and continuum wave functions, and occupation numbers) taken from the average-atom model. The resulting scheme provides a relatively simple diagnostic for use in connection with x-ray scattering measurements. Applications are given to dense hydrogen, beryllium, aluminum, titanium, and tin plasmas. At high momentum transfer, contributions from inelastic scattering by bound electrons are dominant features of the scattered x-ray spectrum for aluminum, titanium, and tin.
We present a model for electron-ion transport in Warm Dense Matter that incorporates Coulomb coupling effects into the quantum Boltzmann equation of Uehling and Uhlenbeck through the use of a statistical potential of mean force. Although this model has been derived rigorously in the classical limit [S.D. Baalrud and J. Daligault, Physics of Plasmas 26, 8, 082106 (2019)], its quantum generalization is complicated by the uncertainty principle. Here we apply an existing model for the potential of mean force based on the quantum Ornstein-Zernike equation coupled with an average-atom model [C. E. Starrett, High Energy Density Phys. 25, 8 (2017)]. This potential contains correlations due to both Coulomb coupling and exchange, and the collision kernel of the kinetic theory enforces Pauli blocking while allowing for electron diffraction and large-angle collisions. By solving the Uehling-Uhlenbeck equation for electron-ion relaxation rates, we predict the momentum and temperature relaxation time and electrical conductivity of solid density aluminum plasma based on electron-ion collisions. We present results for density and temperature conditions that span the transition from classical weakly-coupled plasma to degenerate moderately-coupled plasma. Our findings agree well with recent quantum molecular dynamics simulations.
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