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Register a new userQuantum Mean-Force Kinetic Theory: General Formulation and Application to Electron-Ion Transport in Warm Dense Matter
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We present an approach to extend plasma transport theory into the Warm Dense Matter (WDM) regime characterized by moderate Coulomb coupling and electron degeneracy. It is based on a recently proposed closure of the BBGKY hierarchy that expands in terms of the departure of correlations from their equilibrium value, rather than in terms of the strength of correlations. This kinetic equation contains modifications to the collision term in addition to a second term that models the non-ideal contributions to the equation of state. An explicit collision operator is derived in the semiclassical limit that is similar to that of the Uehling-Uhlenbeck equation, but where scattering is mediated by the potential of mean force (PMF). As a demonstration, we use this collision integral to evaluate temperature and momentum relaxation rates in dense plasmas. We obtain degeneracy- and coupling-dependent Coulomb integrals that take the place of $lnLambda$ in the scattering rates. We additionally find a novel difference in the way in which degeneracy influences momentum relaxation in comparison to temperature relaxation. Finally, we evaluate electron-ion relaxation rates for the case of warm dense deuterium over a range of density and temperature spanning the classical to quantum and weak to strong coupling transitions. Results are compared with the Landau-Spitzer rate and rates obtained from the quantum Landau-Fokker-Planck equation and Lee-More model. We find that the models diverge significantly in the degenerate and moderately coupled regime and attribute this difference to how the various models treat the physics of Pauli blocking, correlations, large-angle scattering, and diffraction.
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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.
We evaluate various analytical models for the electron-ion energy transfer and compare the results to data from molecular dynamics (MD) simulations. The models tested includes energy transfer via strong binary collisions, Landau-Spitzer rates with different choices for the cut-off parameters in the Coulomb logarithm, rates based on Fermis golden rule (FGR) and theories taking coupled collective modes (CM) into account. In search of a model easy to apply, we first analyze different approximations of the FGR energy transfer rate. Then we investigate several numerical studies using MD simulations and try to uncover CM effects in the data obtained. Most MD data published so far show no distinct CM effects and, thus, can be interpreted within a FGR or binary collision approach. We show that this finding is related to the parameter regime, in particular the initial temperature difference, considered in these investigations.
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.
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.
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