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Svensson P, Campbell T, Graziani F, Moldabekov Z, Lyu N, Batista VS, Richardson S, Vinko SM, Gregori G. Development of a new quantum trajectory molecular dynamics framework. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220325. [PMID: 37393934 PMCID: PMC10315217 DOI: 10.1098/rsta.2022.0325] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 01/19/2023] [Indexed: 07/04/2023]
Abstract
An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.
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Affiliation(s)
- Pontus Svensson
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Thomas Campbell
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Frank Graziani
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Zhandos Moldabekov
- Center of Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Ningyi Lyu
- Department of Chemistry, Yale University, New Haven, CT 06520, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, CT 06520, USA
- Yale Quantum Institute, Yale University, New Haven, CT 06511, USA
| | | | - Sam M Vinko
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, UK
| | - Gianluca Gregori
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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Haxhimali T, Rudd RE, Cabot WH, Graziani FR. Shear viscosity for dense plasmas by equilibrium molecular dynamics in asymmetric Yukawa ionic mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:053110. [PMID: 26651805 DOI: 10.1103/physreve.92.053110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2015] [Indexed: 06/05/2023]
Abstract
We present molecular dynamics (MD) calculations of shear viscosity for asymmetric mixed plasma for thermodynamic conditions relevant to astrophysical and inertial confinement fusion plasmas. Specifically, we consider mixtures of deuterium and argon at temperatures of 100-500 eV and a number density of 10^{25} ions/cc. The motion of 30,000-120,000 ions is simulated in which the ions interact via the Yukawa (screened Coulomb) potential. The electric field of the electrons is included in this effective interaction; the electrons are not simulated explicitly. Shear viscosity is calculated using the Green-Kubo approach with an integral of the shear stress autocorrelation function, a quantity calculated in the equilibrium MD simulations. We systematically study different mixtures through a series of simulations with increasing fraction of the minority high-Z element (Ar) in the D-Ar plasma mixture. In the more weakly coupled plasmas, at 500 eV and low Ar fractions, results from MD compare very well with Chapman-Enskog kinetic results. In the more strongly coupled plasmas, the kinetic theory does not agree well with the MD results. We develop a simple model that interpolates between classical kinetic theories at weak coupling and the Murillo Yukawa viscosity model at higher coupling. This hybrid kinetics-MD viscosity model agrees well with the MD results over the conditions simulated, ranging from moderately weakly coupled to moderately strongly coupled asymmetric plasma mixtures.
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Affiliation(s)
- Tomorr Haxhimali
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Robert E Rudd
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - William H Cabot
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Frank R Graziani
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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Grabowski PE, Markmann A, Morozov IV, Valuev IA, Fichtl CA, Richards DF, Batista VS, Graziani FR, Murillo MS. Wave packet spreading and localization in electron-nuclear scattering. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:063104. [PMID: 23848786 DOI: 10.1103/physreve.87.063104] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2013] [Indexed: 06/02/2023]
Abstract
The wave packet molecular dynamics (WPMD) method provides a variational approximation to the solution of the time-dependent Schrödinger equation. Its application in the field of high-temperature dense plasmas has yielded diverging electron width (spreading), which results in diminishing electron-nuclear interactions. Electron spreading has previously been ascribed to a shortcoming of the WPMD method and has been counteracted by various heuristic additions to the models used. We employ more accurate methods to determine if spreading continues to be predicted by them and how WPMD can be improved. A scattering process involving a single dynamic electron interacting with a periodic array of statically screened protons is used as a model problem for comparison. We compare the numerically exact split operator Fourier transform method, the Wigner trajectory method, and the time-dependent variational principle (TDVP). Within the framework of the TDVP, we use the standard variational form of WPMD, the single Gaussian wave packet (WP), as well as a sum of Gaussian WPs, as in the split WP method. Wave packet spreading is predicted by all methods, so it is not the source of the unphysical diminishing of electron-nuclear interactions in WPMD at high temperatures. Instead, the Gaussian WP's inability to correctly reproduce breakup of the electron's probability density into localized density near the protons is responsible for the deviation from more accurate predictions. Extensions of WPMD must include a mechanism for breakup to occur in order to yield dynamics that lead to accurate electron densities.
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Affiliation(s)
- Paul E Grabowski
- Computational Physics and Methods Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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