Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Plasma Physics
Volume 65, Number 11
Monday–Friday, November 9–13, 2020; Remote; Time Zone: Central Standard Time, USA
Session TO06: HED: Warm Dense Matter TheoryLive

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Chair: Suxing Hu, LLE 
Thursday, November 12, 2020 9:30AM  9:42AM Live 
TO06.00001: Hydrodynamic Simulations of LaserInduced Surface Ablation in the Warm Dense Matter Regime Asher Davidson, George Petrov, Daniel Gordon, Joseph Penano Here we use a fully nonlinear hydrodynamic simulation framework, SPARC, to model ablation of metal surfaces by \textasciitilde ps length, \textasciitilde mJ Class lasers. SPARC is a set of modules within a larger, TurboWAVE code, with expanded EquationofState (EOS) capabilities that include solid, liquid, and gaseous states. In problems such as these the laser deposits energy into the conduction band electrons at a much faster rate than the electron and ion temperatures equilibrate, and so a twotemperature model (TTM) is necessary to resolve the physics. The rapid heating of the electrons result in thermionic emission, followed by an electrostatic pull which initiates the ablation process before the ion temperature reaches the melting point. Our choice of EOS for both species will be discussed and elaborated. Special consideration is given to the fact that these electrons are neither a degenerate gas or an ideal plasma, but rather exist in the Warm Dense Matter (WDM) regime. The results of the simulations are benchmarked against experimental results, from which we can extrapolate some of the behaviors of EOS quantities in this intermediate regime while preserving the necessary limiting behaviors. [Preview Abstract] 
Thursday, November 12, 2020 9:42AM  9:54AM Live 
TO06.00002: Simulations of Phonon Modes in LaserPlasma Compressed Solids Oliver Karnbach, Patrick Heighway, Gianluca Gregori, Justin Wark, David McGonegle, Andrew Comley, Rob Rudd Shock and quasiisentropic compression of solidstate matter via laserablation affords the creation of high energy density states of matter, with pressures and temperatures of relevance to core conditions within planets in our own solar system and beyond. Crystallographic phase and density can be discerned via ultrafast xray diffraction, whilst pressure is deduced from VISAR measurements. Temperature is more difficult to determine, but techniques based on inelastic scattering from phonons are being considered [1]. It is in this context that we present here multimillion atom molecular dynamics simulations of the phonons present in fcc crystals shocked beyond their elastic limit. Despite high dislocation densities behind the shock front, distinct phonon modes can still easily be discerned, though such defects do contribute to the quasielastic peak that will compete with any inelastic scattering signal in a real experiment. Changes in the dispersion curves due to compression and the high number of stacking faults can also be observed. [1] E.E. McBride et al., Rev. Sci. Instrum. 89, 10F104 (2018) [Preview Abstract] 
Thursday, November 12, 2020 9:54AM  10:06AM Live 
TO06.00003: Bohm Molecular Dynamics Simulations of Warm Dense Matter Thomas Campbell, Brett Larder, Dirk Gericke, Scott Richardson, Muhammad Kasim, Sam Vinko, Gianluca Gregori The computational demands of modelling large numbers of coupled electrons and ions have long been considered insurmountable, despite advances and refinements in density functional theory (DFT) calculations. However, a different approach to modelling quantum interactions, via application of the Bohmian trajectories formalism, can overcome this hurdle. We present further results from a new Bohm  molecular dynamics approach (Bohm MD). The static results of our simulations are validated by DFT results  our static ionion structure factor of aluminium at 5.2 g cm$^{\mathrm{3}}$ and 3.5 eV shows excellent agreement with both orbital free and Kohn Sham DFT. We then use Bohm MD to extract dynamic results, not only the ionion dynamic structure factor which provides a direct link to experimental observables, but also, unprecedentedly, the ionelectron and electronelectron dynamic structure factors. Thus Bohm MD provides a selfconsistent approach to nonadiabatic investigation of dynamic modes in systems of thousands of particles. [Preview Abstract] 
Thursday, November 12, 2020 10:06AM  10:18AM Live 
TO06.00004: Collisions and Correlation Effects in Warm Dense Matter Thomas Hentschel, Attila Cangi, Andrew Baczewski, Stephanie Hansen The dielectric function calculated within the Random Phase Approximation (RPA) has been applied in many studies to determine the response properties of plasmas, like dynamic structure factors and stopping powers. However, the RPA does not take into account short range electronelectron and electronion interactions which can be important in the warm dense matter regime. To go beyond the RPA, we modify the dielectric function by incorporating electronion collisions and electronic correlations. The collisions are calculated selfconsistently using an averageatom model, while the correlations come from the static local field correction of the uniform electron gas, which was computed by using a path integral Monte Carlo based neural network [Dornheim et al., J. Chem. Phys. 151, 194104 (2019)]. We show how the modified dielectric function changes both dynamic structure factors and stopping powers for charged particles traveling through a plasma and compare with results from experimental data and other theoretical models. [Preview Abstract] 
Thursday, November 12, 2020 10:18AM  10:30AM Live 
TO06.00005: Restricted Configuration Path integral Monte Carlo for warm dense matter Arif Oktay Yilmaz, Kai Hunger, Michael Bonitz, Simon Groth, Tobias Dornheim Quantum Monte Carlo is the most accurate method for simulating the homogeneous electron gas under warm dense matter conditions [T. Dornheim et al., Phys. Reports 744, 186 (2018)] However, due to the notorious fermion sign problem, previous ab initio approaches were restricted to temperatures above half the Fermi temperature, i.e. $\Theta=k_BT/E_F \ge 0.5$. Also, the method of choice for the degenerate Fermi gas  configuration path integral Monte Carlo (CPIMC) [T. Schoof et al., Contrib. Plasma Phys. 51, 687 (2011)]  is restricted to high density, i.e. $r_s=\bar r/a_B \le 1$. Here, we construct two new approximations  RCPIMC and RCPIMC+  that neglect some classes of Monte Carlo updates. While RCPIMC+ reduces the sign problem, RPCIMC completely eliminates it, at the price of a systematic error. We investigate the magnitude of the errors by comparing new finite size corrected [T. Dornheim et al., Phys. Rev. Lett. 117, 156403 (2016)] simulations to the parametrization [S. Groth et al., Phys. Rev. Lett. 115, 135001(2017)]. As a result we conclude that RCPIMC+ allows for accurate simulations of thermodynamic properties (deviations of less than $1\%$) at least up to $r_s = 3$ and $0.05 \le \Theta \le 0.3$, significantly extending the range of CPIMC. [Preview Abstract] 
Thursday, November 12, 2020 10:30AM  10:42AM Live 
TO06.00006: Simulations of Dense Hydrogen and Helium Plasmas Without the FixedNode Approximation Alexey Filinov, Michael Bonitz, Pavel Levashov Quantum Monte Carlo belongs to the most accurate simulation techniques. For Fermi systems, however, its applicability at strong degeneracy is limited by the fermion sign problem. Recently, a significant progress has been achieved for uniform electron gas with configuration path integral Monte Carlo (CPIMC) and permutation blocking (PBPIMC)~[1]. Both methods are free from uncontrolled errors introduced by the fixed nodes approximations. Here we develop a generalization of the PBPIMC~[1] suitable for the grandcanonical ensemble and, in combination with the improved Kelbg potential~[2], perform simulations for hydrogen and helium plasmas down to temperatures 3$\cdot 10^{4}$~K. The obtained isotherms of pressure and internal energy are compared with the restricted PIMC~[3] allowing us to conclude on the accuracy of the fixednode approximation at weak and strong degeneracy, and how the bound state formation affects the results. Some thermodynamic properties are compared with finite temperature DFT simulations~[4]. [1] T.~Dornheim \textit{et al.}, Phys.Rep. {\bf 744}, 186(2018); A.~Filinov \textit{et al.}, Phys.Rev.E {\bf 70}, 046411 (2004); [3] B.~Milizer \textit{et al.}, Phys.Rev.B {\bf 84}, 224109 (2011); [4] D.~Knyazev and, P.~Levashov, Phys. Plasmas {\bf 23}, 102708 (2016). [Preview Abstract] 
Thursday, November 12, 2020 10:42AM  10:54AM Live 
TO06.00007: Nonequilibrium electron dynamics in dense plasmas including dynamical screening and strong coupling Christopher Makait, Niclas Schl\"unzen, JanPhilip Joost, Michael Bonitz The Nonequilibrium Green Functions (NEGF) method is a powerful tool to compute timedependent expectation values of singleparticle observables in correlated quantum manybody systems. Its unfavorable $N_t^3$scaling with propagation time $N_t$ could be reduced to $N_t^2$ by introduction of the Generalized KadanoffBaym Ansatz (GKBA)[1]. Recently, an exact timelocal ($N_t^1$) reformulation of the GKBA, the G1G2 scheme [2,3], has been found for various self energies, which makes this method viable for long time simulations.\\ In a general basis the G1G2 scheme has a computationally expensive scaling with basis size ($N_b^5$$N_b^6$). For the uniform electron gas (UEG) however, we found an advantageous $N_b^3 N_t^1$ scaling for both secondorder and GW selfenergies, which makes this scheme particularly interesting for this system. Here, we present first relaxation results in 1 and 2 dimensions.\\ \quad [1] P. Lipavsk\'y, V. \v{S}pi\v{c}ka, Velick\'y, B, \textit{Phys. Rev. B}34, 6933 (1986)\\ \quad [2] N. Schl\"unzen, JanPhilip Joost, Michael Bonitz, \textit{Phys. Rev. Lett.} 124, 076601 (2020)\\ \quad [3] M. Bonitz, \textit{Quantum Kinetic Theory} (Springer, 2016) [Preview Abstract] 
Thursday, November 12, 2020 10:54AM  11:06AM Live 
TO06.00008: Charge State Fluctuations and Temperature Equilibration in Warm Dense Matter Rory Baggott, Stuart Mangles In warm dense matter, many of the properties are strongly influenced by the charge states of the ions. This is often taken into account by way of the mean ionization or the average charge state populations. However, even in steady state, the number of electrons remaining bound to a particular ion is not constant. Stochastic collisional ionisation and recombination will cause the charge states of ions to fluctuate around their mean. In this work, we use a random walk model to investigate the properties of charge state fluctuations in warm dense matter. A strong dependence on the atomic shell structure is predicted. We also examine the possibility that charge state fluctuations contribute to electronion temperature equilibration by interacting with ion density fluctuations. Despite its importance, temperature equilibration remains poorly understood, with many experimental results yielding disagreements with theory. Preliminary calculations suggest that charge state fluctuations could be a significant factor in understanding temperature relaxation. [Preview Abstract] 
Thursday, November 12, 2020 11:06AM  11:18AM Live 
TO06.00009: A Model for ElectronIon Transport in Dense Plasmas Based on a Mean Force UehlingUhlenbeck Kinetic Equation Shane Rightley, Scott Baalrud Dense plasmas can be subject to electron degeneracy, strong Coulomb coupling, and varying degrees of partial ionization, which makes them difficult to model. We present a method for predicting dense plasma transport using the quantum Boltzmann equation of Uehling and Uhlenbeck, in which the scattering potential is the potential of mean force which is determined by the equilibrium state of the plasma. The dynamics are therefore reduced to those of a binary collision, whereas the potential of mean force can be calculated by any suitable equilibrium method. The method is thus faster than fully dynamical simulations while still containing much of the relevant physics. We apply the method to the calculation of electrical conductivity in dense plasmas; specifically compressed hydrogen and solid density aluminum, each over a range of temperatures spanning above and below the Fermi temperature. Results are compared to alternative models in addition to quantum molecular dynamics simulations in order to validate the model. This work was supported by the U.S. Department of Energy, Office of Fusion Energy Sciences under Award Number DESC0016159. [Preview Abstract] 
Thursday, November 12, 2020 11:18AM  11:30AM Live 
TO06.00010: Accurate Density Functional Theory Simulations Across the WarmDenseMatter Regime: Thermal MetaGGA Exchange Correlation and Nuclear Quantum Effects Valentin Karasiev, Deyan Mihaylov, Suxing Hu Firstprinciples methods based on orbitaldependent and orbitalfree density functional theory take into account the electron quantum effects and provide a compromise between reliability and computational efficiency for simulations of matter across extreme conditions of pressure and temperature in the warmdense matter (WDM) regime. With that, the standard molecular dynamics approach treats ions classically within the BornOppenheimer approximation, omitting nuclear quantum effects (NQE’s). The NQE’s at high pressure are not negligible in a wide range of temperatures and must be taken into account for accurate predictions. In this talk we will discuss recent progress in the development of metageneralized gradient approximation (metaGGA) exchange correlation functional enhanced by the GGAlevel thermal corrections providing improved accuracy across the temperature regimes. Together with quantum treatment of ions via path integral molecular dynamics, our approach provides a systematically improved accuracy of WDM simulations, as we show in an example of dense hydrogen and deuterium plasmas. [Preview Abstract] 
Thursday, November 12, 2020 11:30AM  11:42AM Live 
TO06.00011: A Universal KohnSham Density Functional Theory Approach for Warm Dense Matter Alexander White, Lee Collins Understanding many processes depends strongly on microscopic physics modeling of warm dense matter (WDM) and hot dense plasma. This regime challenges both experiment and analytical modeling, necessitating predictive \emph{ab initio} atomistic computation, typically based on quantum mechanical KohnSham Density Functional Theory (KSDFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the WDM regime. A recentlydeveloped stochastic approach to KSDFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures. We have developed a universal mixed stochasticdeterministic algorithm for DFT at any temperature. This approach leverages the physics of KSDFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated selfconsistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients. LAUR2022738 [Preview Abstract] 
Thursday, November 12, 2020 11:42AM  11:54AM Live 
TO06.00012: Progress in Development of Thermal Hybrid ExchangeCorrelation Density Functionals for Improving the Description of Warm Dense Matter Deyan Mihaylov, Valentin Karasiev, Suxing Hu Recently, it has been shown that explicit dependence on temperature $T$ in the exchangecorrelation (XC) freeenergy density functional is important in density functional theory studies of warm dense matter. As a first approximation, the finite$T$, nonempirical KSDT local spindensity approximation (LSDA) functional was constructed by analytical parametrization of the XC free energy of the homogeneous electron gas. Consequently, the KDT16 generalized gradient approximation (GGA) functional, which captures nonhomogeneity effects and shows better agreement with experiments, was constructed. Here, we present progress in climbing the (finite$T$) Jacob's ladder of XC functional approximations beyond the GGA, by developing a finite$T$ extension of the wellestablished PBE0 and HSE06 hybrids. Application to static calculations of electronic band gap at a wide range of $T$ for various systems of interest to highenergydensity physics show that thermal hybrids provide a significant improvement to the LSDA and GGA rung XC functionals and to the groundstate PBE0 and HSE06 hybrids. [Preview Abstract] 
Thursday, November 12, 2020 11:54AM  12:06PM Live 
TO06.00013: Dynamic properties of the warm dense electron gas: an ab initio path integral Monte Carlo approach Paul Hamann, Tobias Dornheim, Jan Vorberger, Zhandos Moldabekov, Michael Bonitz While being ubiquitous in astrophysics and highly compressed laboratory plasmas, warm dense matter is very difficult to describe theoretically, due to the intricate interplay of quantum degeneracy, correlations and thermal excitations. Abinitio thermodynamic results for the electronic component were obtained only recently [Dornheim et al., Phys. Reports 744, 186 (2018)], using novel path integral Monte Carlo (PIMC) methods. These, however, are limited to static quantities. The investigation of dynamic properties, such as density correlation functions, leading to the dynamic structure factor $S(q,\omega)$  a key quantity measured in xray Thomson scattering experiments  is only feasible in terms of an imaginary time. By carrying out extensive PIMC simulations and developing a new reconstruction method, based on stochastic sampling of the dynamic local field correction, we have recently obtained the first exact quantum Monte Carlo results for the dynamic structure factor [Dornheim et al., Phys. Rev. Lett. 121, 255001 (2018)]. Here we extend this approach to other dynamical quantities of the warm dense electron gas, including the dynamic susceptibility, optical conductivity, and dielectric function. [Preview Abstract] 
Thursday, November 12, 2020 12:06PM  12:18PM Live 
TO06.00014: Ab Initio Results for the Momentum Distribution Function of the Warm Dense Electron Gas Kai Hunger, Tim Schoof, Michael Bonitz The thermodynamics of warm dense matter (WDM) have gained high interest in the past decade due to its significance for technological and astrophysical applications. Theoretically, the electrons pose the most difficulties since quantum and correlation effects are not negligible and can not be approximated with decent accuracy. Recently we have developed the first ab initio Configuration Path Integral Monte Carlo (CPIMC) [1] method for the model of the uniform electron gas (UEG) at finite temperature [2]. Here we extend the CPIMC simulations to the momentum distribution function (MDF) and the static structure factor of the UEG. These structural properties, in particular, a nonexponential highmomentum asymptotics (``quantum tail'') of the MDF, are of crucial importance for scattering cross sections, transport and optical properties. Our simulations confirm the $p^{8}$ asymptotics that was predicted for the ground state and its relation to the socalled ontop pair distribution function [3]. We also present extensive data for the MDF of electrons in the WDM regime, including its values around the Fermi edge. [1] T. Schoof et al., Phys. Rev. Lett. 115, 130402 (2015) [2] T. Dornheim et al., Phys. Reports 744, 186 (2018) [3] J.C. Kimball, J. Phys. A: Math. General 8, 1513 (1975) [Preview Abstract] 
Thursday, November 12, 2020 12:18PM  12:30PM Live 
TO06.00015: Finite temperature density functional theory investigation of the electrical conductivity of warm dense matter with peculiar electronic structure within a twotemperature model Shen Zhang, Hengyu Zhang, Jiayu Dai, Michael Bonitz Density functional theory (DFT) is widely used to investigate the properties of warm dense matter (WDM), including the equation of state, structural properties, as well as transport properties such as thermal and electrical conductivity. However, the common usage of ground state exchange correlation functionals undermines the reliability of DFT calculations since the electron temperature in the WDM regime is far beyond zero. Applying the KuboGreenwood formula, we present a DFT investigation of the electrical conductivity of warm dense lithium, aluminum, copper and gold with peculiar electronic structure that has electron holes for a twotemperature situation, which can be realized in the lab by isochoric heating techniques. Comparing the novel finitetemperature exchange correlation functional (FTXC) of Ref.~\footnote{S. Groth \textit{et al.}, Phys. Rev. Lett. \textbf{119}, 135001 (2017)} with the widely used ground state expressions, we reexamine the temperature effect of electrons in WDM\footnote{M. Bonitz \textit{et al.}, Phys. Plasmas \textbf{27}, 042710 (2020)}. This work is helpful to better understand the physics of related WDM experiments. [Preview Abstract] 
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