Dynamic properties of one-component strongly coupled plasmas: the sum-rule approach

Dynamic properties and the roton mode attenuation in liquid 3He: ab initio study within the self-consistent method of moments

The dynamic structure factor and the eigenmodes of density fluctuations in liquid ³He are studied using a novel non-perturbative approach. This new version of the self-consistent method of moments invokes up to nine sum rules and other exact relations, the two-parameter Shannon information entropy maximization procedure, and the ab initio path integral Monte Carlo simulations which provide necessary reliable input information on the system static properties. Detailed analysis is performed of the collective excitations dispersion relations, the modes' decrements and the static structure factor of ³He at the saturated vapour pressure. The results are compared to available experimental data by Albergamo et al. (Albergamo et al. 2007 Phys. Rev. Lett. 99, 205301. (doi:10.1103/PhysRevLett.99.205301)) and Fåk et al. (Fåk et al. 1994 J. Low Temp. Phys. 97, 445-487. (doi:10.1007/BF00754303)). The theory reveals a clear signature of the roton-like feature in the particle-hole segment of the excitation spectrum with a significant reduction of the roton decrement in the wavenumber range [Formula: see text]. The observed roton mode remains a well-defined collective mode even in the particle-hole band, where it is strongly damped. The existence of the roton-like mode in the bulk liquid ³He is confirmed like in other quantum fluids. The phonon branch of the spectrum is in a reasonable agreement with the same experimental data. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Dynamic characteristics of three-dimensional strongly coupled plasmas

The dynamic structure factor and other dynamic characteristics of strongly coupled one-component plasmas have been studied [Yu. V. Arkhipov et al., Phys. Rev. Lett. 119, 045001 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.045001] using the self-consistent version of the method of moments. Within any version of the latter, the system dielectric function satisfies all involved sum rules and other exact relations automatically, and the advantage of this version is that, in addition, the dynamic characteristics (the dynamic structure factor, the dispersion, and decay parameters of the collective modes) are all expressed in terms of the static ones (the static structure factor) without any adjustment to the simulation data. The approach outlined in the aforementioned Letter is justified in detail and applied mainly to the classical Coulomb systems achieving satisfactory agreement with new numerical simulation data. It is shown how the realm of applicability of the method can be extended to partly degenerate and multicomponent systems, even to simple liquids. Some additional theoretical results are presented in the Supplemental Material.

High-frequency response of classical strongly coupled plasmas

The dynamic structure factor (DSF) of the Yukawa system is here obtained with highly converged molecular dynamics (MD) over the entire liquid phase. The data provide a rigorous test of theoretical models of ion-acoustic wave-dispersion relations, the intermediate scattering function, and the high-frequency response. We compare our MD results with seven diverse models, finding good agreement among those that enforce the three basic sum rules for dispersion properties, although one of the models has previously unreported spurious peaks. The MD simulations reveal that at intermediate frequencies ω, the high-frequency response of the DSF follows a power law, going approximately as ω^{-p}, where p>0, and p shows nontrivial dependencies on the wave vector q and the plasma parameters κ and Γ. In contrast, among the seven comparison models, the predicted high-frequency response is found to be independent of {q,κ,Γ}. This high-frequency power suggests a useful fitting form. In addition, these results expose limitations of several models and, moreover, suggest that some approaches are difficult or impossible to extend because of the lack of finite moments. We also find the double-plasmon resonance peak in our MD simulations that none of the theoretical models predicts.

Ab initio Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter

The accurate description of electrons at extreme density and temperature is of paramount importance for, e.g., the understanding of astrophysical objects and inertial confinement fusion. In this context, the dynamic structure factor S(q,ω) constitutes a key quantity as it is directly measured in x-ray Thomson scattering experiments and governs transport properties like the dynamic conductivity. In this work, we present the first ab initio results for S(q,ω) by carrying out extensive path integral Monte Carlo simulations and developing a new method for the required analytic continuation, which is based on the stochastic sampling of the dynamic local field correction G(q,ω). In addition, we find that the so-called static approximation constitutes a promising opportunity to obtain high-quality data for S(q,ω) over substantial parts of the warm dense matter regime.

Quantum theory for the dynamic structure factor in correlated two-component systems in nonequilibrium: Application to x-ray scattering

We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems.

Direct Determination of Dynamic Properties of Coulomb and Yukawa Classical One-Component Plasmas

Dynamic characteristics of strongly coupled classical one-component Coulomb and Yukawa plasmas are obtained within the nonperturbative model-free moment approach without any data input from simulations so that the dynamic structure factor (DSF) satisfies the first three nonvanishing sum rules automatically. The DSF, dispersion, decay, sound speed, and other characteristics of the collective modes are determined using exclusively the static structure factor calculated from various theoretical approaches including the hypernetted chain approximation. A good quantitative agreement with molecular dynamics simulation data is achieved.

Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime

We use classical molecular dynamics (MD) to study electron-ion temperature equilibration in two-component plasmas in regimes for which the presence of coupled collective modes has been predicted to substantively reduce the equilibration rate. Guided by previous kinetic theory work, we examine hydrogen plasmas at a density of n=10^{26}cm^{-3}, T_{i}=10^{5}K, and 10^{7}K<T_{e}<10^{9}K. The nonequilibrium classical MD simulations are performed with interparticle interactions modeled by quantum statistical potentials (QSPs). Our MD results indicate (i) a large effect from time-varying potential energy, which we quantify by appealing to an adiabatic two-temperature equation of state, and (ii) a notable deviation in the energy equilibration rate when compared to calculations from classical Lenard-Balescu theory including the QSPs. In particular, it is shown that the energy equilibration rates from MD are more similar to those of the theory when coupled modes are neglected. We suggest possible reasons for this surprising result and propose directions of further research along these lines.

Dynamic properties of the energy loss of multi-MeV charged particles traveling in two-component warm dense plasmas

The energy loss of multi-MeV charged particles moving in two-component warm dense plasmas (WDPs) is studied theoretically beyond the random-phase approximation. The short-range correlations between particles are taken into account via dynamic local field corrections (DLFC) in a Mermin dielectric function for two-component plasmas. The mean ionization states are obtained by employing the detailed configuration accounting model. The Yukawa-type effective potential is used to derive the DLFC. Numerically, the DLFC are obtained via self-consistent iterative operations. We find that the DLFC are significant around the maximum of the stopping power. Furthermore, by using the two-component extended Mermin dielectric function model including the DLFC, the energy loss of a proton with an initial energy of ∼15 MeV passing through a WDP of beryllium with an electronic density around the solid value n_{e}≈3×10^{23}cm^{-3} and with temperature around ∼40 eV is estimated numerically. The numerical result is reasonably consistent with the experimental observations [A. B. Zylsta et al., Phys. Rev. Lett. 111, 215002 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.215002]. Our results show that the partial ionization and the dynamic properties should be of importance for the stopping of charged particles moving in the WDP.

Dielectric function of dense plasmas, their stopping power, and sum rules

Mathematical, particularly, asymptotic properties of the random-phase approximation, Mermin approximation, and extended Mermin-type approximation of the coupled plasma dielectric function are analyzed within the method of moments. These models are generalized for two-component plasmas. Some drawbacks and advantages of the above models are pointed out. The two-component plasma stopping power is shown to be enhanced with respect to that of the electron fluid.

Transverse current fluctuations in the Yukawa one-component plasma

Using numerical simulations, we investigate the wave number and frequency dependent transverse current correlation function CT(k,ω) of a single-component fluid with Yukawa interaction potential, also known as the Yukawa one-component plasma. The transverse current correlation function is an important quantity because it contains the microscopic details of the viscoelastic behavior of the fluid. We show that, in the region of densities and temperatures in which shear waves do not propagate, the dynamics of the system are in striking agreement with a simple model of generalized hydrodynamics. As either the density is increased or the temperature decreased, the transverse current correlation function shows additional structure that the simple models fail to capture.

Sum rules for electron-hole bilayer and two-dimensional point dipole systems

We formulate and analyze the third-frequency-moment sum rules for the two-dimensional (point) dipole system (2DDS) and the mass-symmetric electron-hole bilayer (EHB) in their strongly coupled liquid phases. The former, characterized by the repulsive interaction potential φ_{D}(r)=μ^{2}/r^{3} (μ is the electric dipole moment), reasonably well approximates the latter in the d → 0 limit (d is the interlayer spacing), a conjecture that is further supported by the findings of the present work. We explore the extent to which the in-phase sum rule for the closely spaced EHB may or may not reconcile with its 2DDS sum-rule counterpart. This is the main emphasis of the present work.

Quasiparticle parametrization of mean fields, Galilei invariance, and universal conserving response functions

The general possible form of mean-field parametrization in a running frame in terms of current, energy, and density functionals is examined under the restrictions of Galilean invariance. It is found that only two density-dependent parameters remain which are usually condensed in a position-dependent effective mass and the self-energy formed by current and mass. The position-dependent mass induces a position-dependent local current, which is identified for different nonlinear frames. In a second step the response to an external perturbation and relaxation towards a local equilibrium is investigated. The response function is found to be universal in the sense that the actual parametrization of the local equilibrium does not matter and is eliminated from the theory due to the conservation laws. The explicit form of the response with respect to density, momentum, and energy is derived. The compressibility sum rule as well as the sum rule by first- and third-order frequency moments are proved analytically to be fulfilled simultaneously. The results are presented for Bose or Fermi systems in one, two, and three dimensions.

Dynamic ion structure factor of warm dense matter

The dynamics of the ion structure in warm dense matter is determined by molecular dynamics simulations using an effective ion-ion potential. This potential is obtained from ab initio simulations and has a strong short-range repulsion added to a screened Coulomb potential. Models based on static or dynamic local field corrections are found to be insufficient to describe the data. An extended Mermin approach, a hydrodynamic model, and the method of moments with local constraints are capable of reproducing the numerical results but have rather limited predictive powers as they all need some numerical data as input. The method of moments is found to be the most promising.

Density fluctuations in the Yukawa one-component plasma: an accurate model for the dynamical structure factor

Using numerical simulations, we investigate the equilibrium dynamics of a single-component fluid with Yukawa interaction potential. We show that, for a wide range of densities and temperatures, the dynamics of the system are in striking agreement with a simple model of generalized hydrodynamics. Since the Yukawa potential can describe the ion-ion interactions in a plasma, our results have significant applicability for both analyzing and interpreting the results of x-ray scattering data from high-power lasers and fourth-generation light sources.