arXiv subjects

Jan Vorberger

Publications and source records attributed to Jan Vorberger.

At least 91 records · Page 5Linked to original sources

arXiv2023

Revealing Non-equilibrium and Relaxation in Warm Dense Matter

Experiments creating extreme states of matter almost invariably create non-equilibrium states. These are very interesting in their own right but need to be understood even if the ultimate goal is to probe high-pressure or high-temperature equilibrium properties like the equation of state. Here, we report on the capabilities of the newly developed imaginary time correlation function (ITCF) technique [1] to detect and quantify non-equilibrium in pump-probe experiments fielding time resolved x-ray scattering diagnostics. We find a high sensitivity of the ITCF even to a small fraction of non-equilibrium electrons in the Wigner distribution. The behavior of the ITCF technique is such that modern lasers and detectors should be able to trace the non-equilibrium relaxation from tens of femto-seconds to several 10s of picoseconds without the need for a model.

physics.plasm-ph↗

arXiv2023

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.

cond-mat.quant-gas↗

arXiv2023

Linear-response time-dependent density functional theory approach to warm dense matter with adiabatic exchange--correlation kernels

We present a new methodology for the linear-response time-dependent density functional theory (LR-TDDFT) calculation of the dynamic density response function of warm dense matter in an adiabatic approximation that can be used with any available exchange-correlation (XC) functional across Jacob's Ladder and across temperature regimes. The main novelty of the presented approach is that it can go beyond the adiabatic local density approximation (ALDA) and generalized LDA (AGGA) while preserving the self-consistence between the Kohn-Sham (KS) response function and adiabatic XC kernel for extended systems. The key ingredient for the presented method is the combination of the adiabatic XC kernel from the direct perturbation approach with the macroscopic dynamic KS response from the standard LR-TDDFT method using KS orbitals. We demonstrate the application of the method for the example of warm dense hydrogen, for which we perform a detailed analysis of the KS density response function, the RPA result, the total density response function and of the adiabatic XC kernel. The analysis is performed using LDA, GGA, and meta-GGA level approximations for the XC effects. The presented method is directly applicable to disordered systems such as liquid metals, warm dense matter, and dense plasmas.

physics.comp-ph↗

arXiv2023

Extraction of the frequency moments of spectral densities from imaginary-time correlation function data

We introduce an exact framework to compute the positive frequency moments $M^{(α)}(\mathbf{q})=\braket{ω^α}$ of different dynamic properties from imaginary-time quantum Monte Carlo data. As a practical example, we obtain the first five moments of the dynamic structure factor $S(\mathbf{q},ω)$ of the uniform electron gas at the electronic Fermi temperature based on \emph{ab initio} path integral Monte Carlo simulations. We find excellent agreement with known sum rules for $α=1,3$, and, to our knowledge, present the first results for $α=2,4,5$. Our idea can be straightforwardly generalized to other dynamic properties such as the single-particle spectral function $A(\mathbf{q},ω)$, and will be useful for a number of applications, including the study of ultracold atoms, exotic warm dense matter, and condensed matter systems.

cond-mat.quant-gas↗

arXiv2022

Temperature analysis of X-ray Thomson scattering data

The accurate interpretation of experiments with matter at extreme densities and pressures is a notoriously difficult challenge. In a recent work [T.~Dornheim et al., Nature Comm. (in print), arXiv:2206.12805], we have introduced a formally exact methodology that allows extracting the temperature of arbitrarily complex materials without any model assumptions or simulations. Here, we provide a more detailed introduction to this approach and analyze the impact of experimental noise on the extracted temperatures. In particular, we extensively apply our method both to synthetic scattering data and to previous experimental measurements over a broad range of temperatures and wave numbers. We expect that our approach will be of high interest to a gamut of applications, including inertial confinement fusion, laboratory astrophysics, and the compilation of highly accurate equation-of-state databases.

physics.plasm-ph↗

arXiv2022

Ab initio path integral Monte Carlo simulations of hydrogen snapshots at warm dense matter conditions

We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed ion configurations from density functional theory molecular dynamics (DFT-MD) simulations to solve the electronic problem for hydrogen under warm dense matter conditions [M.Böhme et. al. Phys.Rev.Lett.(in print)]. The problem of path collapse due to the Coulomb attraction is avoided by utilizing the pair approximation, which is compared against the simpler Kelbg pair-potential. We find very favourable convergence behaviour towards the former. Since we do not impose any nodal restrictions, our PIMC simulations are afflicted with the notorious fermion sign problem, which we analyse in detail. While computationally demanding, our results constitute an exact benchmark for other methods and approximations such as DFT. Our set-up gives us the unique capability to study important properties of warm dense hydrogen such as the electronic static density response and exchange--correlation (XC) kernel without any model assumptions, which will be very valuable for a variety of applications such as the interpretation of experiments and the development of new XC functionals.

physics.plasm-ph↗

arXiv2022

Electronic Density Response of Warm Dense Matter

Matter at extreme temperatures and pressures -- commonly known as warm dense matter (WDM) in the literature -- is ubiquitous throughout our Universe and occurs in a number of astrophysical objects such as giant planet interiors and brown dwarfs. Moreover, WDM is very important for technological applications such as inertial confinement fusion, and is realized in the laboratory using different techniques. A particularly important property for the understanding of WDM is given by its electronic density response to an external perturbation. Such response properties are routinely probed in x-ray Thomson scattering (XRTS) experiments, and, in addition, are central for the theoretical description of WDM. In this work, we give an overview of a number of recent developments in this field. To this end, we summarize the relevant theoretical background, covering the regime of linear-response theory as well as nonlinear effects, the fully dynamic response and its static, time-independent limit, and the connection between density response properties and imaginary-time correlation functions (ITCF). In addition, we introduce the most important numerical simulation techniques including ab initio path integral Monte Carlo (PIMC) simulations and different thermal density functional theory (DFT) approaches. From a practical perspective, we present a variety of simulation results for different density response properties, covering the archetypal model of the uniform electron gas and realistic WDM systems such as hydrogen. Moreover, we show how the concept of ITCFs can be used to infer the temperature from XRTS measurements of arbitrarily complex systems without the need for any models or approximations. Finally, we outline a strategy for future developments based on the close interplay between simulations and experiments.

physics.plasm-ph↗

arXiv2022

Non-empirical mixing coefficient for hybrid XC functionals from analysis of the XC kernel

We present an analysis of the static exchange-correlation (XC) kernel computed from hybrid functionals with a single mixing coefficient such as PBE0 and PBE0-1/3. We break down the hybrid XC kernels into the exchange and correlation parts using the Hartree-Fock functional, the exchange-only PBE, and the correlation-only PBE. This decomposition is combined with exact data for the static XC kernel of the uniform electron gas and an Airy gas model within a subsystem functional approach. This gives us a tool for the nonempirical choice of the mixing coefficient at ambient and extreme conditions. Our analysis provides physical insights into the effect of the variation of the mixing coefficient in hybrid functionals, which is of immense practical value. The presented approach is general and can be used for other type of functionals like screened hybrids.

physics.chem-ph↗

arXiv2022

Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons

We assess the accuracy of common hybrid exchange-correlation (XC) functionals (PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within Kohn-Sham density functional theory (KS-DFT) for the harmonically perturbed electron gas at parameters relevant for the challenging conditions of warm dense matter. Generated by laser-induced compression and heating in the laboratory, warm dense matter is a state of matter that also occurs in white dwarfs and planetary interiors. We consider both weak and strong degrees of density inhomogeneity induced by the external field at various wavenumbers. We perform an error analysis by comparing to exact quantum Monte-Carlo results. In the case of a weak perturbation, we report the static linear density response function and the static XC kernel at a metallic density for both the degenerate ground-state limit and for partial degeneracy at the electronic Fermi temperature. Overall, we observe an improvement in the density response for partial degeneracy when the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used compared to the previously reported results for the PBE, PBEsol, LDA, AM05, and SCAN functionals; B3LYP, on the other hand, does not perform well for the considered system. Together with the reduction of self-interaction errors, this seems to be the rationale behind the relative success of the HSE03 functional for the description of the experimental data on aluminum and liquid ammonia at WDM conditions.

physics.chem-ph↗

arXiv2022

Ab initio Static Exchange-Correlation Kernel across Jacob's Ladder without functional derivatives

The electronic exchange-correlation (XC) kernel constitutes a fundamental input for the estimation of a gamut of material properties such as the dielectric characteristics, the thermal and electrical conductivity, or the response to an external perturbation. In practice, no reliable method has been known that allows to compute the kernel of real materials with arbitrary XC functionals. In this work, we overcome this long-standing limitation by introducing a new, formally exact methodology for the computation of the material specific static XC kernel exclusively within the framework of density functional theory (DFT) and without employing functional derivatives -- no external input apart from the usual XC-functional is required. We compare our new results with exact quantum Monte Carlo (QMC) data for the archetypical uniform electron gas model at both ambient and warm dense matter conditions. This gives us unprecedented insights into the performance of different XC-functionals, and has important implications for the development of new functionals that are designed for the application at extreme temperatures. In addition, we obtain new DFT results for the XC kernel of warm dense hydrogen as it occurs in fusion applications and astrophysical objects. The observed excellent agreement to the QMC reference data demonstrates that our framework is capable to capture nontrivial effects such as XC-induced isotropy breaking in the density response of hydrogen at large wave numbers.

physics.comp-ph↗

arXiv2022

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.

cond-mat.stat-mech↗

arXiv2022

Accurate Temperature Diagnostics for Matter under Extreme Conditions

The experimental investigation of matter under extreme densities and temperatures as they occur for example in astrophysical objects and nuclear fusion applications constitutes one of the most active frontiers at the interface of material science, plasma physics, and engineering. The central obstacle is given by the rigorous interpretation of the experimental results, as even the diagnosis of basic parameters like the temperature T is rendered highly difficult by the extreme conditions. In this work, we present a simple, approximation-free method to extract the temperature of arbitrarily complex materials from scattering experiments, without the need for any simulations or an explicit deconvolution. This new paradigm can be readily implemented at modern facilities and corresponding experiments will have a profound impact on our understanding of warm dense matter and beyond, and open up a gamut of appealing possibilities in the context of thermonuclear fusion, laboratory astrophysics, and related disciplines.

physics.plasm-ph↗

arXiv2022

Spin-resolved density response of the warm dense electron gas

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) results for the spin-resolved density response of the uniform electron gas (UEG) at warm dense matter conditions. This allows us to unambiguously assess the accuracy of previous theoretical approximations, thereby providing valuable new insights for the future development of dielectric schemes. From a physical perspective, we observe a nontrivial manifestation of an effective electron--electron attraction that emerges in the spin-offdiagonal static density response function at strong coupling, $r_s\gtrsim5$. All PIMC results are freely available online and can be used to benchmark new approximations and simulation schemes.

physics.comp-ph↗

arXiv2022

Effective electronic forces and potentials from ab initio path integral Monte Carlo simulations

The rigorous description of correlated quantum many-body systems constitutes one of the most challenging tasks in contemporary physics and related disciplines. In this context, a particularly useful tool is the concept of effective pair potentials that take into account the effects of the complex many-body medium consistently. In this work, we present extensive, highly accurate \emph{ab initio} path integral Monte Carlo (PIMC) results for the effective interaction and the effective force between two electrons in the presence of the uniform electron gas (UEG). This gives us a direct insight into finite-size effects, thereby opening up the possibility for novel domain decompositions and methodological advances. In addition, we present unassailable numerical proof for an effective attraction between two electrons under moderate coupling conditions, without the mediation of an underlying ionic structure. Finally, we compare our exact PIMC results to effective potentials from linear-response theory, and we demonstrate their usefulness for the description of the dynamic structure factor. All PIMC results are made freely available online and can be used as a thorough benchmark for new developments and approximations.

physics.comp-ph↗

arXiv2022

Electronic pair alignment and roton feature in the warm dense electron gas

The study of matter under extreme densities and temperatures as they occur e.g. in astrophysical objects and nuclear fusion applications has emerged as one of the most active frontiers in physics, material science, and related disciplines. In this context, a key quantity is given by the dynamic structure factor $S(\mathbf{q},ω)$, which is probed in scattering experiments -- the most widely used method of diagnostics at these extreme conditions. In addition to its crucial importance for the study of warm dense matter, the modelling of such dynamic properties of correlated quantum many-body systems constitutes one of the most fundamental theoretical challenges of our time. Here we report a hitherto unexplained \emph{roton feature} in $S(\mathbf{q},ω)$ of the warm dense electron gas, and introduce a microscopic explanation in terms of a new \emph{electronic pair alignment} model. This new paradigm will be highly important for the understanding of warm dense matter, and has a direct impact on the interpretation of scattering experiments. Moreover, we expect our results to give unprecedented insights into the dynamics of a number of correlated quantum many-body systems such as ultracold helium, dipolar supersolids, and bilayer heterostructures.

cond-mat.quant-gas↗

arXiv2022

Electrical Conductivity of Iron in Earth's Core from Microscopic Ohm's Law

Understanding the electronic transport properties of iron under high temperatures and pressures is essential for constraining geophysical processes. The difficulty of reliably measuring these properties under Earth-core conditions calls for sophisticated theoretical methods that can support diagnostics. We present results of the electrical conductivity within the pressure and temperature ranges found in Earth's core from simulating microscopic Ohm's law using time-dependent density functional theory. Our predictions provide a new perspective on resolving discrepancies in recent experiments.

cond-mat.mtrl-sci↗

arXiv2022

Electronic Density Response of Warm Dense Hydrogen: Ab initio Path Integral Monte Carlo Simulations

The properties of hydrogen under extreme conditions are important for many applications, including inertial confinement fusion and astrophysical models. A key quantity is given by the electronic density response to an external perturbation, which is probed in X-ray Thomson scattering (XRTS) experiments -- the state of the art diagnostics from which system parameters like the free electron density $n_e$, the electronic temperature $T_e$, and the charge state $Z$ can be inferred. In this work, we present highly accurate path integral Monte Carlo (PIMC) results for the electronic density response of hydrogen. We obtain the exchange-correlation (XC) kernel $K_{xc}$, which is of central relevance for many applications, such as time-dependent density functional theory (TD-DFT). This gives us a first unbiased look into the electronic density response of hydrogen in the warm-dense matter regime, thereby opening up a gamut of avenues for future research.

physics.comp-ph↗

arXiv2022

Intrinsic energy flow in laser-excited 3$d$ ferromagnets

Ultrafast magnetization dynamics are governed by energy flow between electronic, magnetic, and lattice degrees of freedom. A quantitative understanding of these dynamics must be based on a model that agrees with experimental results for all three subsystems. However, ultrafast dynamics of the lattice remain largely unexplored experimentally. Here, we combine femtosecond electron diffraction experiments of the lattice dynamics with energy-conserving atomistic spin dynamics (ASD) simulations and ab-initio calculations to study the intrinsic energy flow in the 3d ferromagnets cobalt (Co) and iron (Fe). The simulations yield a good description of experimental data, in particular an excellent description of our experimental results for the lattice dynamics. We find that the lattice dynamics are influenced significantly by the magnetization dynamics due to the energy cost of demagnetization. Our results highlight the role of the spin system as the dominant heat sink in the first hundreds of femtoseconds. Together with previous findings for nickel [Zahn et al., Phys. Rev. Research 3, 023032 (2021)], our work demonstrates that energy-conserving ASD simulations provide a general and consistent description of the laser-induced dynamics in all three elemental 3d ferromagnets.

cond-mat.mtrl-sci↗