arXiv subjects

Sebastian Schwalbe

Publications and source records attributed to Sebastian Schwalbe.

At least 19 recordsLinked to original sources

arXiv2026

Kinetic energy from the cubic sum rule of the dynamic structure factor

The third frequency moment sum rule of the dynamic structure factor $S(\mathbf{q},\omega)$ is explored for the first time as an alternative estimator of the kinetic energy $K$ of quantum many-body systems. As a practical example, the uniform electron gas at warm dense matter conditions is considered. First, $K$ is extracted from quasi-exact \emph{ab initio} path integral Monte Carlo results for the imaginary-time density--density correlation function $F(\mathbf{q},\tau)$ and the expected excellent self-consistency with the thermodynamic differentiation route is confirmed. Second, $K$ is extracted from approximate dielectric formalism results for $S(\mathbf{q},\omega)$ and it is observed that common semi-classical approximations lead to a wave-number dependent $K$ with an incorrect short-wavelength limit. Our results are expected to be of broad interest for a great variety of applications, including time-dependent density functional theory, dielectric formalism schemes and warm dense matter models, as well as for the design of dedicated x-ray Thomson scattering experiments with the potential to provide model-free access to the full electronic equation of state.

physics.plasm-ph↗

arXiv2026

X-Ray Diagnostics Analysis Verification and Exploration (xDAVE) Code for the Prediction and Interpretation of X-Ray Thomson Scattering Experiments

X-ray Thomson scattering (XRTS) is a common diagnostic used in the warm dense matter (WDM) regime to estimate plasma parameters like density, temperature and charge state. Experimental analysis typically relies on a forward model to obtain estimates for these parameters, as the measured spectrum is a convolution of the dynamic structure factor (DSF) and the source-instrument function. The Chihara decomposition, where the spectrum is separated into contributions from bound and free electrons, is commonly used to estimate DSFs in the WDM regime, as it allows for the fast calculation of DSFs and therefore can easily be applied in a large-scale parameter optimization. Due to the limited availability of XRTS codes, in this work we present the ``\textbf{X}-ray \textbf{D}iagnostics, \textbf{A}nalysis, \textbf{V}erification and \textbf{E}xploration`` (\texttt{xDAVE}) code, designed to quickly estimate DSFs using the Chihara decomposition and analyse experimental spectra. The code is validated by re-analysing an experiment with isochorically heated beryllium at the OMEGA Laser Facility. In addition, we demonstrate the applicability of the code to plan experiments and predict scattering spectra through the coupling to a ray-tracing code. Lastly, the importance of accounting for the energy-dependence of spectrometer instrument functions is demonstrated by comparing ray-tracing simulations to the standard convolution for strongly compressed Beryllium shots at the National Ignition Facility similar to previously published results.

physics.plasm-ph↗

arXiv2026

Reweighting Estimators for Density Response in Path Integral Monte Carlo: Applications to linear, nonlinear and cross-species density response

We present density response estimators for Monte Carlo simulations that are based on a reweighting procedure, where the samples of an unperturbed system are used to estimate the properties of a system perturbed by an external harmonic potential. This allows the linear and nonlinear static density response to be estimated purely from simulations of the unperturbed system. The method is demonstrated for the uniform electron gas under warm dense matter and strongly coupled conditions using ab initio path integral Monte Carlo simulations. The performance of the method with respect to the number of particles and the number of imaginary time slices is investigated. The scheme is generalised to consider multiple external perturbations, acting on different species and with different wavenumbers, giving one access to additional cross-species density response functions and the complete quadratic response function resolved for both wave number arguments through mode coupling. The flexibility of the methodology opens the possibility to investigate numerous new density response properties to further advance our understanding of interacting quantum many-body systems across a broad range of applications.

physics.chem-ph↗

arXiv2026

Unlocking the Power of Orbital-Free Density Functional Theory to Explore the Electronic Structure Under Extreme Conditions

Recent advances in X-ray free-electron laser diagnostics have enabled direct probing of the electronic structure under extreme pressures and temperatures, such as those encountered in stellar interiors and inertial confinement fusion experiments, challenging theoretical models for interpreting experimental data. Kohn-Sham density functional theory (KSDFT) has been successfully applied to analyze experimental X-ray scattering measurements, but its high computational cost renders routine application impractical. Orbital-free DFT (OFDFT) is a substantially more efficient alternative, with computational cost scaling linearly with system size and a weak temperature dependence, yet it often lacks the accuracy required for electronic structure description. Overcoming this limitation, we present a non-empirical Kohn-Sham-assisted orbital-free density functional framework for calculations at extreme conditions, which enables efficient OFDFT simulations with KSDFT-level accuracy for electron densities, electron-ion structure factors, and equations of state across a broad range of conditions. Benchmark comparisons with quantum Monte Carlo data for dense hydrogen and validation against Rayleigh weight measurements of hot dense beryllium demonstrate the reliability of the framework and speedups of up to several hundred times compared with KSDFT. We further show that even at temperatures on the order of 100 eV, quantum non-locality remains essential for correctly describing the electronic structure of dense hydrogen.

cond-mat.mtrl-sci↗

arXiv2025

Generalized density functional theory framework for the non-linear density response of quantum many-body systems

A density functional theory (DFT) framework is presented that links functional derivatives of free-energy functionals to non-linear static density response functions in quantum many-body systems. Within this framework, explicit expressions are derived for various higher-order response functions of systems that are homogeneous on average, including the first theoretical result for the cubic response at the first harmonic $\chi_0^{(1,3)}(\vec{q})$. Specifically, our framework includes hitherto neglected mode-coupling effects that are important for the non-linear density response even in the presence of a single harmonic perturbation. We compare these predictions for $\chi_0^{(1,3)}(\vec{q})$ to new Kohn-Sham DFT simulations, leading to excellent agreement between theory and numerical results. Exact analytical expressions are also obtained for the long-wavelength limits of the ideal quadratic and cubic response functions. Particular emphasis is placed on the connections between the third- and fourth-order functional derivatives of the non-interacting free-energy functional $F_s[n]$ and the ideal quadratic and cubic response functions of the uniform electron gas, respectively. These relations provide exact constraints that may prove useful for the future construction of improved approximations to $F_s[n]$, in particular for warm dense matter applications at finite temperatures. Here, we use this framework to assess several commonly employed approximations to $F_s[n]$ through orbital-free DFT simulations of the harmonically perturbed ideal electron gas. The results are compared with Kohn-Sham DFT calculations across temperatures ranging from the ground state to the warm dense regime. Additionally, we analyze in detail the temperature- and wavenumber-dependent non-monotonic behavior of the ideal quadratic and cubic response functions.

cond-mat.stat-mech↗

arXiv2025

The noiseless limit and improved-prior limit of the maximum entropy method and their implications for the analytic continuation problem

Quantum Monte Carlo (QMC) methods are uniquely capable of providing exact simulations of quantum many-body systems. Unfortunately, the applications of a QMC simulation are limited because extracting dynamic properties requires solving the analytic continuation (AC) problem. Across the many fields that use QMC methods, there is no universally accepted analytic continuation algorithm for extracting dynamic properties, but many publications compare to the maximum entropy method. We investigate when entropy maximization is an acceptable approach. We show that stochastic sampling algorithms reduce to entropy maximization when the Bayesian prior is near to the true solution. We investigate when is Bryan's controversial optimization algorithm [Bryan, Eur. Biophys. J. 18, 165-174 (1990)] for entropy maximization (sometimes known as the maximum entropy method) appropriate to use. We show that Bryan's algorithm is appropriate when the noise is near zero or when the Bayesian prior is near to the true solution. We also investigate the mean squared error, finding a better scaling when the Bayesian prior is near the true solution than when the noise is near zero. We point to examples of improved data-driven Bayesian priors that have already leveraged this advantage. We support these results by solving the double Gaussian problem using both Bryan's algorithm and the newly formulated dual approach to entropy maximization [Chuna et al., J. Phys. A: Math. Theor. 58, 335203 (2025)].

physics.comp-ph↗

arXiv2025

Spectral Deconvolution without the Deconvolution: Extracting Temperature from X-ray Thomson Scattering Spectra without the Source-and-Instrument Function

X-ray Thomson scattering (XRTS) probes the dynamic structure factor of the system, but the measured spectrum is broadened by the combined source-and-instrument function (SIF) of the setup. In order to extract properties such as temperature from an XRTS spectrum, the broadening by the SIF needs to be removed. Recent work [Dornheim et al. Nature Commun. 13, 7911 (2022)] has suggested that the SIF may be deconvolved using the two-sided Laplace transform. However, the extracted information can depend strongly on the shape of the input SIF, and the SIF is in practice challenging to measure accurately. Here, we propose an alternative approach: we demonstrate that considering ratios of Laplace-transformed XRTS spectra collected at different scattering angles is equivalent to performing the deconvolution, but without the need for explicit knowledge of the SIF. From these ratios, it is possible to directly extract the temperature from the scattering spectra, when the system is in thermal equilibrium. We find the method to be generally robust to spectral noise and physical differences between the spectrometers, and we explore situations in which the method breaks down. Furthermore, the fact that consistent temperatures can be extracted for systems in thermal equilibrium indicates that non-equilibrium effects could be identified by inconsistent temperatures of a few eV between the ratios of three or more scattering angles.

physics.plasm-ph↗

arXiv2025

Enhancing the Efficiency of Time-Dependent Density Functional Theory Calculations of Dynamic Response Properties

X-ray Thomson scattering (XRTS) constitutes an essential technique for diagnosing material properties under extreme conditions, such as high pressures and intense laser heating. Time-dependent density functional theory (TDDFT) is one of the most accurate available ab initio methods for modeling XRTS spectra, as well as a host of other dynamic material properties. However, strong thermal excitations, along with the need to account for variations in temperature and density as well as the finite size of the detector significantly increase the computational cost of TDDFT simulations compared to ambient conditions. In this work, we present a broadly applicable method for optimizing and enhancing the efficiency of TDDFT calculations. Our approach is based on a one-to-one mapping between the dynamic structure factor and the imaginary time density--density correlation function, which naturally emerges in Feynman's path integral formulation of quantum many-body theory. Specifically, we combine rigorous convergence tests in the imaginary time domain with a constraints-based attenuation of narrow-band fluctuations to improve the efficiency of TDDFT modeling without the introduction of any significant bias. As a result, we can report a speed-up by up to an order of magnitude, thus substantially reducing the burden of computational cost required for XRTS analysis.

cond-mat.mtrl-sci↗

arXiv2025

Correlation function metrology for warm dense matter: Recent developments and practical guidelines

X-ray Thomson scattering (XRTS) has emerged as a valuable diagnostic for matter under extreme conditions, as it captures the intricate many-body physics of the probed sample. Recent advances, such as the model-free temperature diagnostic of Dornheim et al. [Nat.Commun. 13, 7911 (2022)], have demonstrated how much information can be extracted directly within the imaginary-time formalism. However, since the imaginary-time formalism is a concept often difficult to grasp, we provide here a systematic overview of its theoretical foundations and explicitly demonstrate its practical applications to temperature inference, including relevant subtleties. Furthermore, we present recent developments that enable the determination of the absolute normalization, Rayleigh weight, and density from XRTS measurements without reliance on uncontrolled model assumptions. Finally, we outline a unified workflow that guides the extraction of these key observables, offering a practical framework for applying the method to interpret experimental measurements.

physics.plasm-ph↗

arXiv2025

Taylor series perspective on ab initio path integral Monte Carlo simulations with Fermi-Dirac statistics

The fermion sign problem constitutes a fundamental computational bottleneck across a plethora of research fields in physics, quantum chemistry and related disciplines. Recently, it has been suggested to alleviate the sign problem in \emph{ab initio} path integral Molecular Dynamics and path integral Monte Carlo (PIMC) calculations based on the simulation of fictitious identical particles that are represented by a continuous quantum statistics variable $\xi$ [\textit{J.~Chem.~Phys.}~\textbf{157}, 094112 (2022)]. This idea facilitated a host of applications including the interpretation of an x-ray scattering experiment with strongly compressed beryllium at the National Ignition Facility [\textit{Nature Commun.}~\textbf{16}, 5103 (2025)]. In the present work, we express the original isothermal $\xi$-extrapolation method as a special case of a truncated Taylor series expansion around the $\xi=0$ limit of distinguishable particles. We derive new PIMC estimators that allow us to evaluate the Taylor coefficients up to arbitrary order and we carry out extensive new PIMC simulations of the warm dense electron gas to systematically analyze the sign problem from this new perspective. This gives us important insights into the applicability of the $\xi$-extrapolation method for different levels of quantum degeneracy in terms of the Taylor series radius of convergence. Moreover, the direct PIMC evaluation of the $\xi$-derivatives, in principle, removes the necessity for simulations at different values of $\xi$ and can facilitate more efficient simulations that are designed to maximize compute time in those regions of the full permutation space that contribute most to the final Taylor estimate of the fermionic expectation value of interest.

physics.chem-ph↗

arXiv2025

Re-weighting estimator for ab initio path integral Monte Carlo simulations of fictitious identical particles

The fermion sign problem constitutes one of the most fundamental obstacles in quantum many-body theory. Recently, it has been suggested to circumvent the sign problem by carrying out path integral simulations with a fictitious quantum statistics variable $\xi$, which allows for a smooth interpolation between the bosonic and fermionic limits [\textit{J.~Chem.~Phys.}~\textbf{157}, 094112 (2022)]. This $\xi$-extrapolation method has subsequently been applied to a variety of systems and has facilitated the analysis of an x-ray scattering measurement taken at the National Ignition Facility with unprecedented accuracy [\textit{Nature Commun.}~\textbf{16}, 5103 (2025)]. Yet, it comes at the cost of performing an additional $10-20$ simulations, which, in combination with the required small error bars, can pose a serious practical limitation. Here, we remove this bottleneck by presenting a new re-weighting estimator, which allows the study of the full $\xi$-dependence from a single path integral Monte Carlo (PIMC) simulation. This is demonstrated for various observables of the uniform electron gas and also warm dense beryllium. We expect our work to be useful for future PIMC simulations of Fermi systems, including ultracold atoms, electrons in quantum dots, and warm dense quantum plasmas.

physics.chem-ph↗

arXiv2025

Orientational Effects in the Low Pair Continuum of Aluminium

We compare the predictions of the dynamic structure factor (DSF) of ambient polycrystalline aluminium from time-dependent density functional theory (TDDFT) in the pair continuum regime to recent ultrahigh resolution x-ray Thomson scattering measurements, collected at the European XFEL. TDDFT predicts strong anisotropy in the DSF at the wavenumber examined here, even with $q$-blurring accounted for. The experimental spectrum has more than sufficient resolution and signal-to-noise levels to resolve these orientation dependencies, and therefore the orientational averaging of the polycrystalline sample is observed rigorously. Once the orientation averaging is accounted for, TDDFT is able to reproduce the experimental spectrum adequately. Finally, comparisons of predicted DSFs from jellium to experiment demonstrates the importance of accounting for lattice effects in modelling the spectrum from a polycrystal.

cond-mat.mtrl-sci↗

arXiv2025

Ab initio density functional theory approach to warm dense hydrogen: from density response to electronic correlations

Understanding the properties of warm dense hydrogen is of key importance for the modeling of compact astrophysical objects and to understand and further optimize inertial confinement fusion (ICF) applications. The work horse of warm dense matter theory is given by thermal density functional theory (DFT), which, however, suffers from two limitations: (i) its accuracy can depend on the utilized exchange--correlation (XC) functional, which has to be approximated and (ii) it is generally limited to single-electron properties such as the density distribution. Here, we present a new ansatz combining time-dependent DFT results for the dynamic structure factor $S_{ee}(\mathbf{q},\omega)$ with static DFT results for the density response. This allows us to estimate the electron--electron static structure factor $S_{ee}(\mathbf{q})$ of warm dense hydrogen with high accuracy over a broad range of densities and temperatures. In addition to its value for the study of warm dense matter, our work opens up new avenues for the future study of electronic correlations exclusively within the framework of DFT for a host of applications.

physics.plasm-ph↗

arXiv2025

Static linear density response from X-ray Thomson scattering measurements: a case study of warm dense beryllium

Linear response theory is ubiquitous throughout physics and plays a central role in the theoretical description of warm dense matter -- an extreme state that occurs within compact astrophysical objects and that is traversed on the compression path of a fuel capsule in inertial confinement fusion applications. Here we show how one can relate the static linear density response function to X-ray Thomson scattering (XRTS) measurements, which opens up new possibilities for the diagnostics of extreme states of matter, and for the rigorous assessment and verification of theoretical models and approximations. As a practical example, we consider an XRTS data set of warm dense beryllium taken at the National Ignition Facility [T.~D\"oppner \emph{et al.}, \textit{Nature} \textbf{618}, 270-275 (2023)]. The comparison with state-of-the-art \emph{ab initio} path integral Monte Carlo (PIMC) simulations [T.~Dornheim \emph{et al.}, \textit{Nature Commun.}~(in print), arXiv:2402.19113] gives us a best estimate of the mass density of $\rho=18\pm6\,$g/cc, which is consistent with previous PIMC and density functional theory based studies, but rules out the original estimate of $\rho=34\pm4\,$g/cc based on a Chihara model fit.

physics.plasm-ph↗

arXiv2025

HEART: A New X-Ray Tracing Code for Mosaic Crystal Spectrometers

We introduce a new open-source Python x-ray tracing code for modelling Bragg diffracting mosaic crystal spectrometers: High Energy Applications Ray Tracer (HEART). HEART's high modularity enables customizable workflows as well as efficient development of novel features. Utilizing Numba's just-in-time (JIT) compiler and the message-passing interface (MPI) allows running HEART in parallel leading to excellent performance. HEART is intended to be used for modelling x-ray spectra as they would be seen in experiments that measure x-ray spectroscopy with a mosaic crystal spectrometer. This enables the user to make predictions about what will be seen on a detector in experiment, perform optimizations on the design of the spectrometer setup, or to study the effect of the spectrometer on measured spectra. However, the code certainly has further uses beyond these example use cases. Here, we discuss the physical model used in the code, and explore a number of different mosaic distribution functions, intrinsic rocking curves, and sampling approaches which are available to the user. Finally, we demonstrate its strong predictive capability in comparison to spectroscopic data collected at the European XFEL in Germany.

physics.plasm-ph↗

arXiv2025

Estimating ionization states and continuum lowering from ab initio path integral Monte Carlo simulations for warm dense hydrogen

Warm dense matter (WDM) is an active field of research, with applications ranging from astrophysics to inertial confinement fusion. Ionization degree and continuum lowering are important quantities to understand how materials behave under these conditions, but can be difficult to diagnose since experimental campaigns are limited and often require model-dependent analysis. This is especially true for hydrogen, which has a comparably low scattering cross section, making high quality data particularly difficult to obtain. Consequently, building equation of state tables often relies on exact simulations in combination with untested approximations to extract properties from experiments. Here, we investigate an approach for extracting the ionization potential depression and ionization degree -- quantities which are otherwise not directly accessible from the physical model -- from exact ab initio path integral Monte Carlo (PIMC) simulations utilizing a chemical model. In contrast to experimental measurements, where noise and non-equilibrium effects add to the uncertainty of the inferred parameters, PIMC simulations provide a clean signal with well-defined thermodynamic conditions. Comparisons against commonly used models show a qualitative agreement, but we find deviations primarily for the high density and high temperature cases. We also demonstrate the decreasing sensitivity of the dynamic structure factor with respect to both ionization and continuum lowering for increasing scattering angles in x-ray Thomson scattering experiments. Our work has important implications for the design of future experiments, but also offers qualitative understanding of structure factors and the imaginary-time correlation function obtained from exact quantum Monte Carlo simulations.

physics.chem-ph↗

arXiv2025

Fermionic free energies from \textit{ab initio} path integral Monte Carlo simulations of fictitious identical particles

We combine the recent $\eta-$ensemble path integral Monte Carlo (PIMC) approach to the free energy [T.~Dornheim \textit{et al.}, \textit{Phys.~Rev.~B} \textbf{111}, L041114 (2025)] with a recent fictitious partition function technique based on inserting a continuous variable that interpolates between the bosonic and fermionic limits [Xiong and Xiong, \textit{J.~Chem.~Phys.}~\textbf{157}, 094112 (2022)] to deal with the fermion sign problem. As a practical example, we apply our set-up to the warm dense uniform electron gas over a broad range of densities and temperatures. We obtain accurate results for the exchange--correlation free energy down to half the Fermi temperature, and find excellent agreement with the state-of-the-art parametrization by Groth \textit{et al.}~[\textit{Phys.~Rev.~Lett.}~\textbf{119}, 135001 (2017)]. Our work opens up new avenues for the future study of a host of interacting Fermi-systems, including warm dense matter, ultracold atoms, and electrons in quantum dots.

cond-mat.quant-gas↗

arXiv2025

Applying the Liouville-Lanczos Method of Time-Dependent Density-Functional Theory to Warm Dense Matter

Ab initio modeling of dynamic structure factors (DSF) and related density response properties in the warm dense matter (WDM) regime is a challenging computational task. The DSF, convolved with a probing X-ray beam and instrument function, is measured in X-ray Thomson scattering (XRTS) experiments, which allows for the study of electronic structure properties at the microscopic level. Among the various ab initio methods, linear response time-dependent density functional theory (LR-TDDFT) is a key framework for simulating the DSF. The standard approach in LR-TDDFT for computing the DSF relies on the orbital representation. A significant drawback of this method is the unfavorable scaling of the number of required empty bands as the wavenumber increases, making LR-TDDFT impractical for modeling XRTS measurements over large energy scales, such as in backward scattering geometry. We consider and test an alternative approach that employs the Liouville-Lanczos (LL) method for simulating the DSF. This approach does not require empty states and allows the DSF at large momentum transfer values and over a broad frequency range to be accessed. We compare the results obtained from the LL method with those from the standard LR-TDDFT within the projector augmented-wave formalism for isochorically heated aluminum and warm dense hydrogen. Additionally, we utilize exact path integral Monte Carlo (PIMC) results for the imaginary-time density-density correlation function (ITCF) of warm dense hydrogen to rigorously benchmark the LL approach. We discuss the application of the LL method for calculating DSFs and ITCFs at different wavenumbers, the effects of pseudopotentials, and the role of Lorentzian smearing. The successful validation of the LL method under WDM conditions makes it a valuable addition to the ab initio simulation landscape, supporting experimental efforts and advancing WDM theory.

physics.plasm-ph↗