Session UM10: Mini-conference: Dense Quantum Plasma Simulation I

Path Integral Monte Carlo and Density Functional Molecular Dynamics Simulations of Warm Dense Matter

We analyze the applicability of two first-principles simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), to study the regime of warm dense matter. We discuss the advantages as well as the limitations of each method and propose directions for future development. Results for dense, liquid helium, where both methods have been applied [1-3], demonstrate the range of each method's applicability. Comparison of the equations of state from simulations with analytical theories and free energy models show that DFT is useful for temperatures below 100000 K and then PIMC provides accurate results for all higher temperatures. We characterize the structure of the liquid in terms of pair correlation functions and study the closure of the band gap with increasing density and temperature. Finally, we discuss simulations of heavier elements and demonstrate the reliability are both methods in such cases with preliminary results. \\[4pt] [1] B. Militzer, Phys. Rev. Lett. 97 (2006) 175501. \\[0pt] [2] B. Militzer, Phys. Rev. B 79 (2009) 106407. \\[0pt] [3] B. Militzer, J Phys. A 42 (2009) 214001.   

Quantum Molecular Dynamics calculation of electrical and thermal transport properties

Dense, strongly-coupled plasmas, with degenerate or partially degenerate electrons --- ubiquitous in high energy density physics, inertial fusion, planetary science, and warm dense matter --- are very difficult to describe accurately with traditional theoretical approaches. Over the last decade, density functional based molecular dynamics, also know as quantum molecular dynamics (QMD), has emerged as a powerful tool for the study of dense quantum plasmas, providing accurate equation of state, structural, and transport properties. This talk will focus on the QMD calculation of electrical and thermal conductivities with a much higher degree of accuracy than was possible with earlier methods. Within the density functional approach, electrical and thermal conductivities are extracted directly from the electronic orbitals using the Kubo-Greenwood and Chester-Thellung formalisms, circumventing the need to define the ionization states and collision cross sections. These transport calculations have now been used to generate several wide-range transport models for use in large-scale simulation codes, allowing unprecedented simulations of complex experiments. Sandia National Laboratories is a multi program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Mass Transport in the Warm, Dense Matter and High-Energy Density Regimes

Large-scale hydrodynamical simulations of fluids and plasmas under extreme conditions require knowledge of certain microscopic properties such as diffusion and viscosity in addition to the equation-of-state. To determine these dynamical properties, we employ quantum molecular dynamical (MD) simulations on large samples of atoms. The method has several advantages: 1) static, dynamical, and optical properties are produced consistently from the same simulations, and 2) mixture properties arise in a natural way since all intra- and inter-particle interactions are properly represented. We utilize two forms of density functional theory: 1) Kohn-Sham (KS-DFT) and 2) orbital-free (OF-DFT). KS-DFT is computationally intense due to its reliance on an orbital representation. As the temperature rises, the Thomas-Fermi approximation in OF-DFT begins to represent accurately the density functional, and provides an efficient and systematic means for extending the quantum simulations to very hot conditions. We have performed KS-DFT and OF-DFT calculations of the self-diffusion, mutual diffusion and shear viscosity for Al, Li, H, and LiH. We examine trends in these quantities and compare to more approximate forms such as the one-component plasma model. We also determine the validity of mixing rules that combine the properties of pure species into a composite result.   

Properties of hot dense plasmas by Orbital-Free Molecular Dynamics

During the last decade DFT calculations have been successfully applied to the WDM regime. To overcome the limitations of DFT in temperature and density we propose to return to the very basis of DFT by using an ``only on the density'' formulation of the electronic kinetic energy, essentially captured by the finite temperature formulation of the Thomas-Fermi theory. High temperatures (up to few KeV) and high densities (up to 10$\times \rho_0$) systems can be addressed by orbital free molecular dynamics simulations (OFMD) at the expense of a fine description of atomic properties such as binding properties. Thanks to an efficient numerical scheme, up to thousands of particles can be propagated giving accurate static and dynamical properties without any assumptions on the ionization state or on the screening of interactions. Simulations of hydrogen and iron up to 5~keV and boron up to 10 times the normal density were performed. Very dissymmetrical mixtures can be also treated without difficulties. More recently, this method has been applied to hydrogen at high density (up to 160\,g/cc) and high temperature (up to 1 KeV) to generate long trajectories for a later computation of the thermal conductivity with classical DFT. This method bridges the gap between quantum and classical molecular dynamics in the field of hot-dense plasmas and could be also used as a platform to include more physics such as nuclear reactions or interaction with a radiative field.   

Strongly-correlated quantum-plasma simulations via classical maps and density-functional theory - going beyond big codes

A nominally ``high-temperature'' plasma may be a ``cold quantum system" if the ratio $T/E_F<1$, where $T$ is the temperature (energy units), and $E_F$ is the Fermi energy. The electron spin and possible ionization states $Z^{i+}$ require multi-component simulations versatile enough for quantum, classical and thermal effects, bound states, etc., when e-e, e-ion and ion-ion interactions are not weak. In {\it ab initio} calculations, the densities and $T$ (or several subsytem temperatures) are inputs. The outputs are the equation of state, transport and optical properties. Density-functional-theory (DFT) and molecular-dynamics (MD) based simulations via codes like VASP (Vienna ab-initio simulation package) treat a small number of particles in a box. These methods do not accurately implement e-e pair correlations. The particle statistics are poor for multi-component systems. The computational effort is very large and demanding. We present simpler methods using liquid structure theory, classical maps of quantum systems, and DFT to establish simple, accurate computational procedures for highly correlated multi-component systems. Such quantum calculations for jellium at $T=0$, finite-$T$ high density H-plasmas and Al-plasmas, are contrasted with equivalent calculations from Quantum Monte-Carlo, or VASP-based simulations.   

Restricted Path-Integral Molecular Dynamics for Simulating the Correlated Electron Plasma in Warm Dense Matter

Several areas of study including heavy ion beam, large scale laser, and high pressure or Thomson scattering studies necessitate a fundamental understanding of warm dense matter (WDM) i.e. matter at high temperature and high density. The WDM regime, however, lacks any adequate highly developed class of simulation methods. Recent progress to address this deficit has been the development of orbital-free Density Functional Theory (ofDFT). However, scant benchmark information is available on temperature and pressure dependence of simple but realistic models in WDM regime. The present work aims to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Within the discrete path integral representation, electrons are described as harmonic necklaces. Quantum exchange takes the form of cross linking between electron necklaces. The fermion sign problem is addressed by restricting the density matrix to positive values. The molecular dynamics algorithm is employed to sample phase space. Here, we focus on the behavior of strongly correlated electron plasmas under WDM conditions. We compute the kinetic and potential energies and compare them to those obtained with the ofDFT method.   

Molecular Dynamics of Hot Dense Plasmas: New Horizons

We describe the status of a new time-dependent simulation capability for hot dense plasmas. The backbone of this multi-institutional computational and experimental effort---the Cimarron Project---is the massively parallel molecular dynamics (MD) code ``ddcMD''. The project's focus is material conditions such as exist in inertial confinement fusion experiments, and in many stellar interiors: high temperatures, high densities, significant electromagnetic fields, mixtures of high- and low-$Z $elements, and non-Maxwellian particle distributions. Of particular importance is our ability to incorporate into this classical MD code key atomic, radiative, and nuclear processes, so that their interacting effects under non-ideal plasma conditions can be investigated. This talk summarizes progress in computational methodology, discusses strengths and weaknesses of quantum statistical potentials as effective interactions for MD, explains the model used for quantum events possibly occurring in a collision and highlights some significant results obtained to date.