Quantum fluid description of dense plasmas

Two-component dense quantum plasmas are created in various experimental facilities by means of compression of matter by charged particles or laser beams. These experiments are motivated by the problem of inertial confinement fusion and the investigation of the physics of massive astrophysical objects. The simultaneous importance of thermal excitations and electronic quantum and correlation effects makes a theoretical study of dense quantum plasmas challenging. Ab initio methods such as Quantum Monte Carlo and Kohn-Sham density functional theory are, currently, not able to serve as a tool for the large scale simulation of dense quantum plasmas due to the large computational effort. Therefore, quantum hydrodynamics (QHD) has gained attention as a possible method to circumvent this restriction and, thus, to carry out large scale simulations. However, it appeared that QHD suffers from a lack of a reliable theoretical foundation and has not yet been generalized to finite temperatures. With the aforementioned shortcomings, we have to consider QHD as a unreliable method to simulate high-energy-density plasmas. Therefore, the thesis at hand presents the first consistent derivation of finite temperature QHD for fermions and the first unifying picture to the various previously used versions of the QHD. Moreover, linking with the linear response theory, the results presented in this thesis go beyond all previous considerations by providing a consistent derivation of the fully non-local potentials taking into account the electronic exchange-correlation effects for both low frequency and high frequency phenomena. Further, in order to verify the importance of the electronic quantum non-locality and correlations, different existing approximations describing the electronic density response function have been implemented to study the structural properties of strongly coupled ions.Zweikomponentige, dichte Quantenplasmen werden in verschiedenen Versuchsanlagen erzeugt. Dabei wird Materie durch Laser oder hochenergetische B\"undel geladener Teilchen komprimiert. Motiviert sind diese Experimente durch Arbeiten an der Tr\"agheitsfusion und der Untersuchung der physikalischen Eigenschaften massereicher astrophysikalischer Objekte. Die gleichzeitige Bedeutung von thermischen Anregungen und elektronischen Quanten- und Korrelationseffekten macht eine theoretische Untersuchung von dichten Quantenplasmen \"au{\ss}erst schwierig. Ab initio-Methoden wie Quantum Monte Carlo und die Kohn-Sham-Dichtefunktionaltheorie sind derzeit aufgrund des hohen erforderlichen Rechenaufwands nicht in der Lage, als Werkzeug f\"ur gro{\ss}skalige Simulation von dichten Quantenplasmen zu dienen. Daher hat die Quantenhydrodynamik (QHD) als m\"ogliche Methode zur Umgehung dieser Einschr\"ankungen und damit zur Durchf\"uhrung von gro{\ss}skaligen Computersimulationen an Bedeutung gewonnen. Es zeigt sich jedoch, dass es der QHD an verl\"asslichen theoretischen Grundlagen mangelt und sie noch nicht auf endliche Temperaturen verallgemeinert wurde. Deshalb muss die QHD als unzuverl\"assige Methode zur Simulation von hochenergetischen Plasmen angesehen werden. Dadurch motiviert, gibt die vorliegende Arbeit eine erste konsequente Ableitung der fermionischen QHD f\"ur endliche Temperaturen und die erste Vereinheitlichung verschiedener zuvor verwendeter Versionen der QHD. Weiterhin gehen die Ergebnisse dieser Arbeit, durch die Verkn\"upfung mit der Linear-Response-Theorie sowie eine konsequente Ableitung vollst\"andig nicht-lokaler Potenziale unter Ber\"ucksichtigung der elektronischen Austausch-Korrelations-Effekte f\"ur niederfrequente und hochfrequente Ph\"anomene, \"uber alle bisherigen Arbeiten hinaus

Transverse magnetic field influence on wakefield in complex plasmas

We present the results of an investigation of the wakefield around a stationary charged grain in an external magnetic field with non-zero transverse component with respect to the ion flow direction. The impact of the orientation of magnetic field on the wake behavior in streaming complex plasmas is assessed. In contrast to previously reported significant suppression of the wake oscillations due to longitudinal magnetic field applied along flow, in the presence of transverse to flow magnetic field the wakefield exhibits a long range recurrent oscillations. Extensive investigation for a wide range of parameters reveal that in the sonic and supersonic regimes the wake has strong dependence on the direction of the magnetic field and exhibits sensitivity to even a meager deviation of magnetic field from the longitudinal orientation. The tool obtained with the study of impact of transverse component of magnetic field on the wake around grain in streaming ions can be used to potentially maneuver the grain-grain interaction to achieve controlled grain dynamics.Comment: PIC, complex plasma, dust in streaming magnetized ions, monte-carlo, dusty plasma

Energy response and spatial alignment of the perturbed electron gas

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulations of the harmonically perturbed uniform electron gas (UEG) for different densities and temperatures. This allows us to study the linear response of the UEG with respect to different contributions to the total energy for different wave numbers. We find that the induced change in the interaction energy exhibits a non-monotonic behaviour, and becomes negative for intermediate wave numbers. This effect is strongly dependent on the coupling strength and can be traced back to the spatial alignment of electrons introduced in earlier works [T.~Dornheim \emph{et al.}, Communications Physics \textbf{5}, 304 (2022)]. The observed quadratic dependence on the perturbation amplitude in the limit of weak perturbations and the quartic dependence of the perturbation amplitude corrections are consistent with linear and non-linear versions of the density stifness theorem. All PIMC simulation results are freely available online and can be used to benchmark new methods, or as input for other calculations

Analyzing X-ray Thomson scattering experiments of warm dense matter in the imaginary-time domain: theoretical models and simulations

The rigorous diagnostics of experiments with warm dense matter (WDM) is notoriously difficult. A key method is given by X-ray Thomson scattering (XRTS), but the interpretation of XRTS measurements is usually based on theoretical models that entail various approximations. Recently, Dornheim et al. [arXiv:2206.12805] have introduced a new framework for temperature diagnostics of XRTS experiments that is based on imaginary-time correlation functions (ITCF). On the one hand, switching from the frequency- to the imaginary-time domain gives one direct access to a number of physical properties, which facilitates the extraction of the temperature of arbitrarily complex materials without any models or approximations. On the other hand, the bulk of theoretical works in dynamic quantum many-body theory is devoted to the frequency-domain, and, to our knowledge, the manifestation of physics properties within the ITCF remains poorly understood. In the present work, we aim to change this unsatisfactory situation by introducing a simple, semi-analytical model for the imaginary-time dependence of two-body correlations within the framework of imaginary-time path integrals. As a practical example, we compare our new model to extensive ab initio path integral Monte Carlo results for the ITCF of a uniform electron gas, and find excellent agreement over a broad range of wave numbers, densities, and temperatures

Averaging over atom snapshots in linear-response TDDFT of disordered systems: A case study of warm dense hydrogen

Linear-response time-dependent density functional theory (LR-TDDFT) simulations of disordered extended systems require averaging over different snapshots of ion configurations to minimize finite size effects due to the snapshot--dependence of the electronic density response function and related properties. We present a consistent scheme for the computation of the macroscopic Kohn-Sham (KS) density response function connecting an average over snapshot values of charge density perturbations to the averaged values of KS potential variations. This allows us to formulate the LR-TDDFT within the adiabatic (static) approximation for the exchange-correlation (XC) kernel for disordered systems, where the static XC kernel is computed using the direct perturbation method [Moldabekov et al., J. Chem. Theory Comput. 19, 1286 (2023)]. The presented approach allows one to compute the macroscopic dynamic density response function as well as the dielectric function with a static XC kernel generated for any available XC functional. The application of the developed workflow is demonstrated for the example of warm dense hydrogen. The presented approach is applicable for various types of extended disordered systems such as warm dense matter, liquid metals, and dense plasmas

Electronic density response of warm dense hydrogen on the nanoscale

The properties of hydrogen at warm dense matter (WDM) conditions are of high importance for the understanding of astrophysical objects and technological applications such as inertial confinement fusion. In this work, we present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) results for the electronic properties in the Coulomb potential of a fixed ionic configuration. This gives us new insights into the complex interplay between the electronic localization around the protons with their density response to an external harmonic perturbation. We find qualitative agreement between our simulation data and a heuristic model based on the assumption of a local uniform electron gas model, but important trends are not captured by this simplification. In addition to being interesting in their own right, we are convinced that our results will be of high value for future projects, such as the rigorous benchmarking of approximate theories for the simulation of WDM, most notably density functional theory