Generalized hydrodynamics model for strongly coupled plasmas

Abstract

Beginning with the exact equations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, we obtain the density, momentum, and stress tensor-moment equations. We close the moment equations with two closures, one that guarantees an equilibrium state given by density-functional theory and another that includes collisions in the relaxation of the stress tensor. The introduction of a density functional-theory closure ensures self-consistency in the equation-of-state properties of the plasma (ideal and excess pressure, electric fields, and correlations). The resulting generalized hydrodynamics thus includes all impacts of Coulomb coupling, viscous damping, and the high-frequency (viscoelastic) response. We compare our results with those of several known models, including generalized hydrodynamic theory and models obtained using the Singwi-Tosi-Land-Sjolander approximation and the quasilocalized charge approximation. We find that the viscoelastic response, including both the high-frequency elastic generalization and viscous wave damping, is important for correctly describing ion-acoustic waves. We illustrate this result by considering three very different systems: ultracold plasmas, dusty plasmas, and dense plasmas. The new model is validated by comparing its results with those of the current autocorrelation function obtained from molecular-dynamics simulations of Yukawa plasmas, and the agreement is excellent. Generalizations of this model to mixtures and quantum systems should be straightforward.

Gapped momentum states

“…Refs. [65,67,68] for review and references therein). We do not attempt to review this large field, but instead remark that, similarly to liquids, the kgap seen in molecular dynamics simulations of plasma models (see, e.g.…”

“…Theoretically, the gapped momentum states in plasma are rationalized using generalized hydrodynamics, the approach that extends the hydrodynamic description to larger k and ω (see, e.g., [70,68,76]) as in liquids mentioned earlier and discussed in section 7.1 in more detail. Interestingly, the authors of Ref.…”

The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation

“…Consequently, finding an accurate theory for the LFC has been a long-standing problem for decades [34,35]. Such information is crucial for * t.dornheim@hzdr.de many applications, including the interpretation of experiments [36][37][38][39][40], the construction of effective, electronically screened potentials [41][42][43], the development of advanced functionals for DFT [44][45][46][47], the incorporation of electronic correlations into quantum hydrodynamics [48][49][50], and the calculation of other material properties like electrical and thermal conductivities [51,52], stopping power [53,54], and energy transfer rates [55].…”

Ab initio path integral monte carlo simulation of the uniform electron gas in the high energy density regime

“…Here χ 0 (q, ω) denotes the density response function of the ideal (i.e., noninteracting) system that is known from theory [1], and G(q, ω) is the local field correction (LFC) that includes the complete, wave number-resolved description of exchange-correlation effects. Consequently, the LFC is of paramount importance for many applications, such as the calculation of electrical and thermal conductivities [63,64], the construction of effective potentials [65,66,67], the incorporation of correlation effects into quantum hydrodynamics [68,69,70,28], and the development of advanced exchange-correlation functionals for DFT [71,72,73,74]. Very recently, we have achieved a major breakthrough by presenting a machinelearning based representation of the static LFC G(q) = G(q, 0) covering the entire relevant WDM regime, 0.7 ≤ r s ≤ 20.…”