arXiv subjects

Burkhard Militzer

Publications and source records attributed to Burkhard Militzer.

71 records · Page 4Linked to original sources

arXiv2012

All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas

We develop an all-electron path integral Monte Carlo (PIMC) method with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. We thereby extend PIMC studies beyond hydrogen and helium to elements with core electrons. PIMC pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics (DFT-MD) at temperatures of (2.5-7.5)$\times10^5$ K and both methods together form a coherent equation of state (EOS) over a density-temperature range of 3--12 g/cm$^3$ and 10$^4$--10$^9$ K.

cond-mat.mtrl-sci↗

arXiv2011

Erosion of icy cores in giant gas planets

Using ab initio simulations we investigate whether water ice is stable in the cores of giant planets, or whether it dissolves into the layer of metallic hydrogen above. By Gibbs free energy calculations we find that for pressures between 10 and 40 Mbar the ice-hydrogen interface is unstable at temperatures above approximately 3000 K, far below the temperature of the core-mantle boundaries in Jupiter and Saturn that are of the order of 10000 K. This implies that the cores of solar and extrasolar giant planets are at least partially eroded.

astro-ph.EP↗

arXiv2011

Rocky core solubility in Jupiter and giant exoplanets

Gas giants are believed to form by the accretion of hydrogen-helium gas around an initial protocore of rock and ice. The question of whether the rocky parts of the core dissolve into the fluid H-He layers following formation has significant implications for planetary structure and evolution. Here we use ab initio calculations to study rock solubility in fluid hydrogen, choosing MgO as a representative example of planetary rocky materials, and find MgO to be highly soluble in H for temperatures in excess of approximately 10000 K, implying significant redistribution of rocky core material in Jupiter and larger exoplanets.

astro-ph.EP↗

arXiv2010

New Phases of Water Ice Predicted at Megabar Pressures

Based on density functional calculations we predict water ice to attain two new crystal structures with Pbca and Cmcm symmetry at 7.6 and 15.5 Mbar, respectively. The known high pressure ice phases VII, VIII, X, and Pbcm as well as the Pbca phase are all insulating and composed of two interpenetrating hydrogen bonded networks, but the Cmcm structure is metallic and consists of corrugated sheets of H and O atoms. The H atoms are squeezed into octahedral positions between next-nearest O atoms while they occupy tetrahedral positions between nearest O atoms in the ice X, Pbcm, and Pbca phases.

cond-mat.mtrl-sci↗

arXiv2010

Sequestration of noble gases in giant planet interiors

The Galileo probe showed that Jupiter's atmosphere is severely depleted in neon compared to protosolar values. We show, via ab initio simulations of the partitioning of neon between hydrogen and helium phases, that the observed depletion can be explained by the sequestration of neon into helium-rich droplets within the postulated hydrogen-helium immiscibility layer of the planet's interior. We also demonstrate that this mechanism will not affect argon, explaining the observed lack of depletion of this gas. This provides strong indirect evidence for hydrogen-helium immiscibility in Jupiter.

astro-ph.EP↗

arXiv2009

Giant Planet Interior Structure and Thermal Evolution

We discuss the interior structure and composition of giant planets, and how this structure changes as these planets cool and contract over time. Here we define giant planets as those that have an observable hydrogen-helium envelope, which includes Jupiter-like planets, which are predominantly H/He gas, and Neptune-like planets which are predominantly composed of elements heavier than H/He. We describe the equations of state of planetary materials and the construction of static structural models and thermal evolution models. We apply these models to transiting planets close to their parent stars, as well as directly imaged planets far from their parent stars. Mechanisms that have been postulated to inflate the radii of close-in transiting planets are discussed. We also review knowledge gained from the study of the solar system's giant planets. The frontiers of giant planet physics are discussed with an eye towards future planetary discoveries.

astro-ph.EP↗

arXiv2009

Correlations in Hot Dense Helium

Hot dense helium is studied with first-principles computer simulations. By combining path integral Monte Carlo and density functional molecular dynamics, a large temperature and density interval ranging from 1000 to 1000000 K and 0.4 to 5.4 g/cc becomes accessible to first-principles simulations and the changes in the structure of dense hot fluids can be investigated. The focus of this article are pair correlation functions between nuclei, between electrons, and between electrons and nuclei. The density and temperature dependence of these correlation functions is analyzed in order to describe the structure of the dense fluid helium at extreme conditions.

cond-mat.mtrl-sci↗

arXiv2008

First-Principles Studies of the Metallization and the Equation of State of Solid Helium

The insulator-to-metal transition in solid helium at high pressure is studied with first-principles simulations. Diffusion quantum Monte Carlo (DMC) calculations predict that the band gap closes at a density of 21.3 g/cc and a pressure of 25.7 terapascals, which is 20% higher in density and 40% higher in pressure than predicted by density functional calculations based on the generalized gradient approximation (GGA). The metallization density derived from GW calculations is found to be in very close agreement with DMC predictions. The zero point motion of the nuclei had no effect on the metallization density within the accuracy of the calculation. Finally, fit functions for the equation of state are presented and the magnitude of the electronic correlation effects left out of the GGA approximation are discussed.

physics.comp-ph↗

arXiv2007

Implications of Shock Wave Experiments with Precompressed Materials for Giant Planet Interiors

This work uses density functional molecular dynamics simulations of fluid helium at high pressure to examine how shock wave experiments with precompressed samples can help characterizing the interior of giant planets. In particular, we analyze how large of a precompression is needed to probe a certain depth in a planet's gas envelope. We find that precompressions of up to 0.1, 1.0, 10, or 100 GPa are needed to characterized 2.5, 5.9, 18, to 63% of Jupiter's envelope by mass.

cond-mat.mtrl-sci↗

arXiv2007

Properties of Dense Fluid Hydrogen and Helium in Giant Gas Planets

Equilibrium properties of hydrogen-helium mixtures under thermodynamic conditions found in the interior of giant gas planets are studied by means of density functional theory molecular dynamics simulations. Special emphasis is placed on the molecular-to-atomic transition in the fluid phase of hydrogen in the presence of helium. Helium has a substantial influence on the stability of hydrogen molecules. The molecular bond is strengthened and its length is shortened as a result of the increased localization of the electron charge around the helium atoms, which leads to more stable hydrogen molecules compared to pure hydrogen for the same thermodynamic conditions. The {\it ab initio} treatment of the mixture enables us to investigate the structure of the liquid and to discuss hydrogen-hydrogen, helium-helium, and hydrogen-helium correlations on the basis of pair correlation functions.

cond-mat.mtrl-sci↗

arXiv2005

Simulations of Dense Atomic Hydrogen in the Wigner Crystal Phase

Path integral Monte Carlo simulations are applied to study dense atomic hydrogen in the regime where the protons form a Wigner crystal. The interaction of the protons with the degenerate electron gas is modeled by Thomas-Fermi screening, which leads to a Yukawa potential for the proton-proton interaction. A numerical technique for the derivation of the corresponding action of the paths is described. For a fixed density of rs=200, the melting is analyzed using the Lindemann ratio, the structure factor and free energy calculations. Anharmonic effects in the crystal vibrations are analyzed.

cond-mat.mtrl-sci↗

arXiv2004

Hydrogen-Helium Mixtures at High Pressure

The properties of hydrogen-helium mixtures at high pressure are crucial to address important questions about the interior of Giant planets e.g. whether Jupiter has a rocky core and did it emerge via core accretion? Using path integral Monte Carlo simulations, we study the properties of these mixtures as a function of temperature, density and composition. The equation of state is calculated and compared to chemical models. We probe the accuracy of the ideal mixing approximation commonly used in such models. Finally, we discuss the structure of the liquid in terms of pair correlation functions.

cond-mat.mtrl-sci↗

arXiv2003

Structure and bonding of dense liquid oxygen from first principles simulations

Using first principles simulations we have investigated the structural and bonding properties of dense fluid oxygen up to 180 GPa. We have found that band gap closure occurs in the molecular liquid, with a "slow" transition from a semi-conducting to a poor metallic state occurring over a wide pressure range. At approximately 80 GPa, molecular dissociation is observed in the metallic fluid. Spin fluctuations play a key role in determining the electronic structure of the low pressure fluid, while they are suppressed at high pressure.

cond-mat.mtrl-sci↗

arXiv2002

Calculation of Shock Hugoniot Curves of Precompressed Liquid Deuterium

Path integral Monte Carlo simulations have been used to study deuterium at high pressure and temperature. The equation of state has been derived in the temperature and density region of 10000 < T < 1000000 K and 0.6 < rho < 2.5 gcm-3. A series of shock Hugoniot curves is computed for different initial compressions in order to compare with current and future shock wave experiments using liquid deuterium samples precompressed in diamond anvil cells.

cond-mat.stat-mech↗

arXiv2002

Lowering of the Kinetic Energy in Interacting Quantum Systems

Interactions never lower the ground state kinetic energy of a quantum system. However, at nonzero temperature, where the system occupies a thermal distribution of states, interactions can reduce the kinetic energy below the noninteracting value. This can be demonstrated from a first order weak coupling expansion. Simulations (both variational and restricted path integral Monte Carlo) of the electron gas model and dense hydrogen confirm this and show that in contrast to the ground state case, at nonzero temperature the population of low momentum states can be increased relative to the free Fermi distribution. This effect is not seen in simulations of liquid He-3.

cond-mat.stat-mech↗

arXiv1999

Characterization of the State of Hydrogen

Fermionic path integral Monte Carlo simulations have been applied to study the equilibrium properties of the hydrogen and deuterium in the density and temperature range of 1.6 < rs < 14.0 and 5000K < T < 167000K. We use this technique to determine the phase diagram by identifying the plasma, the molecular, atomic and metallic regime. We explain how one can identify the phases in the path integral formalism and discuss the state of hydrogen for 5 points in the temperature-density plane. Further we will provide arguments for the nature of the transitions between the regimes.

physics.plasm-ph↗

arXiv1999

Variational Density Matrix Method for Warm Condensed Matter and Application to Dense Hydrogen

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.

physics.plasm-ph↗