arXiv subjects

Zhandos Moldabekov

Publications and source records attributed to Zhandos Moldabekov.

52 records · Page 3Linked to original sources

arXiv2022

The uniform electron gas at high temperatures: \emph{ab initio} path integral Monte Carlo simulations and analytical theory

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) in the high-temperature regime, $8\leqθ=k_\textnormal{B}T/E_\textnormal{F}\leq128$. This allows us to study the convergence of different properties towards the classical limit. In particular, we investigate the classical relation between the static structure factor $S(\mathbf{q})$ and the static local field correction $G(\mathbf{q})$, which is only fulfilled at low densities. Moreover, we compare our new results for the interaction energy to the parametrization of the UEG by Groth \emph{et al.}~[PRL \textbf{119}, 135001 (2017)], which interpolates between PIMC results for $θ\leq8$ and the Debye-Hückel limit, and to higher order analytical virial expansions. Finally, we consider the momentum distribution function $n(\mathbf{q})$ and find an interaction-induced increase in the occupation of the zero-momentum state even for $θ\gtrsim32$. All PIMC data are freely available online, and can be used as input for improved parametrizations and as a rigorous benchmark for approximate methods.

physics.plasm-ph↗

arXiv2022

Density-Functional-Theory Perspective on the Non-Linear Response of Correlated Electrons Across Temperature Regimes

We explore a new formalism to study the nonlinear electronic density response based on Kohn-Sham density functional theory (KS-DFT) at partially and strongly quantum degenerate regimes. It is demonstrated that the KS-DFT calculations are able to accurately reproduce the available path integral Monte Carlo simulation results at temperatures relevant for warm dense matter research. The existing analytical results for the quadratic and cubic response functions are rigorously tested. It is demonstrated that the analytical results for the quadratic response function closely agree with the KS-DFT data. Furthermore, the performed analysis reveals that currently available analytical formulas for the cubic response function are not able to describe simulation results, neither qualitatively nor quantitatively, at small wave-numbers $q<2q_F$, with $q_F$ being the Fermi wave-number. The results show that KS-DFT can be used to describe warm dense matter that is strongly perturbed by an external field with remarkable accuracy. Furthermore, it is demonstrated that KS-DFT constitutes a valuable tool to guide the development of the non-linear response theory of correlated quantum electrons from ambient to extreme conditions. This opens up new avenues to study nonlinear effects in a gamut of different contexts at conditions that cannot be accessed with previously used path integral Monte Carlo methods [T. Dornheim et al., Phys. Rev. Lett. 125, 085001 (2020)].

physics.plasm-ph↗

arXiv2021

Nonlinear electronic density response of the warm dense electron gas: multiple perturbations and mode coupling

We present extensive new ab initio path integral Monte Carlo (PIMC) results for an electron gas at warm dense matter conditions that is subject to multiple harmonic perturbations. In addition to the previously investigated nonlinear effects at the original wave number [Dornheim \emph{et al.}, PRL \textbf{125}, 085001 (2020)] and the excitation of higher harmonics [Dornheim \emph{et al.}, PRR \textbf{3}, 033231 (2021)], the presence of multiple external potentials leads to mode-coupling effects, which constitute the dominant nonlinear effect and lead to a substantially more complicated density response compared to linear response theory. One possibility to estimate mode-coupling effects from a PIMC simulation of the unperturbed system is given in terms of generalized imaginary-time correlation functions that have been recently introduced by Dornheim \emph{et al.}~[JCP \textbf{155}, 054110 (2021)]. In addition, we extend our previous analytical theory of the nonlinear density response of the electron gas in terms of the static local field correction [Dornheim \emph{et al.}, PRL \textbf{125}, 235001 (2020)], which allows for a highly accurate description of the PIMC results with negligible computational cost.

physics.plasm-ph↗

arXiv2021

Benchmarking Exchange-Correlation Functionals in the Spin-Polarized Inhomogeneous Electron Gas under Warm Dense Conditions

Warm dense matter is a highly active research area both at the frontier and interface of material science and plasma physics. We assess the performance of commonly used exchange-correlation (XC) approximation (LDA, PBE, PBEsol, and AM05) in the spin-polarized inhomogeneous electron gas under warm dense conditions based on exact path-integral quantum Monte-Carlo calculations. This extends our recent analysis on the relevance of inhomogeneities in the spin-unpolarized warm dense electron gas [Z.~Moldabekov et al., J. Chem. Phys. 155, 124116 (2021)]. We demonstrate that the predictive accuracy of these XC functionals deteriorates with (1) a decrease in density (corresponding to an increase in the inter-electronic correlation strength) and (2) an increase of the characteristic wave number of the density perturbation. We provide recommendations for the applicability of the considered XC functionals at conditions typical for warm dense matter. Furthermore, we hint at future possibilities for constructing more accurate XC functionals under these conditions.

physics.plasm-ph↗

arXiv2021

Path Integral Monte Carlo Simulations of liquid $^3$He without Fixed Nodes: Structural Properties and Collective Excitations

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulations of normal liquid $^3$He without any nodal constraints. This allows us to study the effects of temperature on different structural properties like the static structure factor $S(\mathbf{q})$, the momentum distribution $n(\mathbf{q})$, and the static density response function $χ(\mathbf{q})$, and to unambiguously quantify the impact of Fermi statistics. In addition, the dynamic structure factor $S(\mathbf{q},ω)$ is rigorously reconstructed from imaginary-time PIMC data, and we find the familiar phonon-maxon-roton dispersion that is well known from $^4$He and has been reported previously for two-dimensional $^3$He films [Nature \textbf{483}, 576-579 (2012)]. The comparison of our new results for both $S(\mathbf{q})$ and $S(\mathbf{q},ω)$ to neutron scattering measurements reveals an excellent agreement between theory and experiment.

physics.comp-ph↗

arXiv2021

The Relevance of Electronic Perturbations in the Warm Dense Electron Gas

Warm dense matter (WDM) has emerged as one of the frontiers of both experimental and theoretical physics and is challenging traditional concepts of plasma, atomic, and condensed-matter physics. While it has become common practice to model correlated electrons in WDM within the framework of Kohn-Sham density functional theory, quantitative benchmarks of exchange-correlation (XC) functionals under WDM conditions are yet incomplete. Here, we present the first assessment of common XC functionals against exact path-integral Monte Carlo calculations of the harmonically perturbed thermal electron gas. This system is directly related to the numerical modeling of X-Ray scattering experiments on warm dense samples. Our assessment yields the parameter space where common XC functionals are applicable. More importantly, we pinpoint where the tested XC functionals fail when perturbations on the electronic structure are imposed. We indicate the lack of XC functionals that take into account the needs of WDM physics in terms of perturbed electronic structures.

physics.plasm-ph↗

arXiv2021

Nonlinear Density Response and Higher Order Correlation Functions in Warm Dense Matter

In a recent letter [\textit{Phys.~Rev.~Lett.}~\textbf{125}, 085001 (2020)], Dornheim \textit{et al.}~have presented the first \textit{ab initio} path integral Monte Carlo (PIMC) results for the nonlinear electronic density response at warm dense matter (WDM) conditions. In the present work, we extend these considerations by exploring the relation between the nonlinear response and three-/four-body correlation functions from many-body theory. In particular, this connection directly implies a comparably increased sensitivity of the nonlinear response to electronic exchange-correlation (XC) effects, which is indeed confirmed by our analysis over the entire relevant range of densities ($r_s=0.5,\dots,10$) and temperatures ($θ=0.01,\dots,4$). Finally, our work suggests the possibility of deliberately probing the nonlinear regime to experimentally probe three- and potentially even four-body correlation functions in WDM.

physics.plasm-ph↗

arXiv2021

Nonlinear electronic density response of the ferromagnetic uniform electron gas at warm dense matter conditions

In a recent Letter [T.~Dornheim \emph{et al.}, Phys.~Rev.~Lett.~\textbf{125}, 085001 (2020)], we have presented the first \emph{ab initio} results for the nonlinear density response of electrons in the warm dense matter regime. In the present work, we extend these efforts by carrying out extensive new path integral Monte Carlo (PIMC) simulations of a \emph{ferromagnetic} electron gas that is subject to an external harmonic perturbation. This allows us to unambiguously quantify the impact of spin-effects on the nonlinear density response of the warm dense electron gas. In addition to their utility for the description of warm dense matter in an external magnetic field, our results further advance our current understanding of the uniform electron gas as a fundamental model system, which is important in its own right.

physics.plasm-ph↗

arXiv2021

A Machine-Learning Surrogate Model for ab initio Electronic Correlations at Extreme Conditions

The electronic structure in matter under extreme conditions is a challenging complex system prevalent in astrophysical objects and highly relevant for technological applications. We show how machine-learning surrogates in terms of neural networks have a profound impact on the efficient modeling of matter under extreme conditions. We demonstrate the utility of a surrogate model that is trained on \emph{ab initio} quantum Monte Carlo data for various applications in the emerging field of warm dense matter research.

physics.comp-ph↗

arXiv2020

Screening of a test charge in a free-electron gas at warm dense matter and dense non-ideal plasma conditions

The screening of a test charge by partially degenerate non-ideal free electrons at conditions related to warm dense matter and dense plasmas is investigated using linear response theory and the local field correction based on ab inito Quantum Monte-Carlo simulations data. The analysis of the obtained results is performed by comparing to the random phase approximation and the Singwi-Tosi-Land-Sjölander approximation. The applicability of the long-wavelength approximation for the description of screening is investigated. The impact of electronic exchange-correlations effects on structural properties and the applicability of the screened potential from linear response theory for the simulation of the dynamics of ions are discussed.

physics.plasm-ph↗

arXiv2020

Ab initio results for the plasmon dispersion and damping of the warm dense electron gas

Warm dense matter (WDM) is an exotic state on the border between condensed matter and dense plasmas. Important occurrences of WDM include dense astrophysical objects, matter in the core of our Earth, as well as matter produced in strong compression experiments. As of late, x-ray Thomson scattering has become an advanced tool to diagnose WDM. The interpretation of the data requires model input for the dynamic structure factor $S(q,ω)$ and the plasmon dispersion $ω(q)$. Recently the first \textit{ab initio} results for $S(q,ω)$ of the homogeneous warm dense electron gas were obtained from path integral Monte Carlo simulations, [Dornheim \textit{et al.}, Phys. Rev. Lett. \textbf{121}, 255001 (2018)]. Here, we analyse the effects of correlations and finite temperature on the dynamic dielectric function and the plasmon dispersion. Our results for the plasmon dispersion and damping differ significantly from the random phase approximation and from earlier models of the correlated electron gas. Moreover, we show when commonly used weak damping approximations break down and how the method of complex zeros of the dielectric function can solve this problem for WDM conditions.

physics.plasm-ph↗

arXiv2020

Ab initio path integral Monte Carlo simulation of the Uniform Electron Gas in the High Energy Density Regime

The response of the uniform electron gas (UEG) to an external perturbation is of paramount importance for many applications. Recently, highly accurate results for the static density response function and the corresponding local field correction have been provided both for warm dense matter [\textit{J.~Chem.~Phys.}~\textbf{151}, 194104 (2019)] and strongly coupled electron liquid [\textit{Phys.~Rev.~B}~\textbf{101}, 045129 (2020)] conditions based on exact \textit{ab initio} path integral Monte Carlo (PIMC) simulations. In the present work, we further complete our current description of the UEG by exploring the high energy density regime, which is relevant for, e.g., astrophysical applications and inertial confinement fusion experiments. To this end, we present extensive new PIMC results for the static density response in the range of $0.05 \leq r_s \leq 0.5$ and $0.85\leqθ\leq8$. These data are subsequently used to benchmark the accuracy of the widely used random phase approximation and the dielectric theory by Singwi, Tosi, Land, and Sjölander (STLS). Moreover, we compare our results to configuration PIMC data where they are available and find perfect agreement with a relative accuracy of $0.001-0.01\%$. All PIMC data are available online.

physics.comp-ph↗

arXiv2019

The Static Local Field Correction of the Warm Dense Electron Gas: An ab Initio Path Integral Monte Carlo Study and Machine Learning Representation

The study of matter at extreme densities and temperatures as they occur in astrophysical objects and state-of-the art experiments with high-intensity lasers is of high current interest for many applications. While no overarching theory for this regime exists, accurate data for the density response of correlated electrons to an external perturbation are of paramount importance. In this context, the key quantity is given by the local field correction (LFC), which provides a wave-vector resolved description of exchange-correlation effects. In this work, we present extensive new path integral Monte Carlo (PIMC) results for the static LFC of the uniform electron gas, which are subsequently used to train a fully connected deep neural network. This allows us to present a continuous representation of the LFC with respect to wave-vector, density, and temperature covering the entire warm dense matter regime. Both the PIMC data and neural-net results are available online. Moreover, we expect the presented combination of ab initio calculations with machine-learning methods to be a promising strategy for many applications.

physics.plasm-ph↗

arXiv2019

Plasma-grains interaction mediated by streaming non-Maxwellian ions

A comprehensive parametric study of plasma-grain interaction for non-Maxwellian streaming ions in steady-state employing particle-in-cell simulations is delineated. Instead of considering the inter-grain interaction potential to be the linear sum of isolated grain potentials, we incorporate the numerical advancement developed fully for grain shielding by including nonlinear contributions from the plasma and shadowing effect. The forces acting on grains versus inter-grain distance, streaming velocity of the ions, and impact of trapped ions density (number) are characterized for non- Maxwellian ions in the presence of charge-exchange collisions. It is found that the nonlinear plasma response considerably modifies the plasma-grains interaction. Unlike the stationary plasma case, for two identical grains separated by a distance in the presence of streaming ions, the electrostatic force is neither repulsive for all grain separations nor equivalent to the force due to one isolated grain. Inadequacy of the linear response formalism in dealing with the systems having very large grain charges is also discussed. The smallest inter-grain separation for which the role of the shadow effect can be ignored is reported.

physics.plasm-ph↗

arXiv2015

Statically screened ion potential and Bohm potential in a quantum plasma

The effective potential $Φ$ of a classical ion in a weakly correlated quantum plasma in thermodynamic equilibrium at finite temperature is well described by the RPA screened Coulomb potential. Additionally, collision effects can be included via a relaxation time ansatz (Mermin dielectric function). These potentials are used to study the quality of various statically screened potentials that were recently proposed by Shukla and Eliasson (SE) [Phys. Rev. Lett. {\bf 108}, 165007 (2012)], Akbari--Moghanjoughi (AM) [Phys. Plasmas {\bf 22}, 022103 (2015)] and Stanton and Murillo (SM) [Phys. Rev. E {\bf 91}, 033104 (2015)] starting from quantum hydrodynamic theory (QHD). Our analysis reveals that the SE potential is qualitatively different from the full potential, whereas the SM potential (at any temperature) and the AM potential (at zero temperature) are significantly more accurate. This confirms the correctness of the recently derived [Michta {\em et al.}, Contrib. Plasma Phys. {\bf 55}, (2015)] pre-factor $1/9$ in front of the Bohm term of QHD for fermions.

physics.plasm-ph↗

arXiv2014

The ion potential in warm dense matter: wake effects due to streaming degenerate electrons

The effective dynamically screened potential of a classical ion in a stationary flowing quantum plasma at finite temperature is investigated. This is a key quantity for thermodynamics and transport of dense plasmas in the warm dense matter regime. This potential has been studied before within hydrodynamic approaches or based on the zero temperature Lindhard dielectric function. Here we extend the kinetic analysis by including the effects of finite temperature and of collisions based on the Mermin dielectric function. The resulting ion potential exhibits an oscillatory structure with attractive minima (wakes) and, thus, strongly deviates from the static Yukawa potential of equilibrium plasmas. This potential is analyzed in detail for high-density plasmas with values of the Brueckner parameter in the range $0.1 \le r_s \le 1$, for a broad range of plasma temperature and electron streaming velocity. It is shown that wake effects become weaker with increasing temperature of the electrons. Finally, we obtain the minimal electron streaming velocity for which attraction between ions occurs. This velocity turns out to be less than the electron Fermi velocity. Our results allow, for the first time, for reliable predictions of the strength of wake effects in nonequilibrium quantum plasmas with fast streaming electrons showing that these effects are crucial for transport under warm dense matter conditions, in particular for laser-matter interaction, electron-ion temperature equilibration and for stopping power.

physics.plasm-ph↗