Jan Vorberger

Since its first successful applications in the early 2000s, X-ray Thomson scattering (XRTS) has emerged as one of the most successful tools for the diagnostics of extreme states of matter in the laboratory. By sampling the dynamic structure factor of the electrons, XRTS is capable of giving detailed insights into the atomic-scale physics of the matter probed. Moreover, thermodynamic parameters, such as the mass density, temperature, and ionization state, are routinely inferred from XRTS measurements, providing a comprehensive characterization of the sample probed. In addition, the dynamic structure factor is of considerable interest in its own right, since it contains information on other effects such as the plasmon shift, miscibility between species, electronic states, and potential transitions between these states. In this work, we provide an extensive overview of previous XRTS experiments at both traditional laser and X-ray free-electron laser facilities, including information about the probed material (elements and conditions), scattering geometry, and analysis methods, as well as the corresponding references. In addition, we briefly discuss the advantages and shortcomings of widely used analysis methods for XRTS spectra and reflect on upcoming future developments in XRTS experiments and theory.

The year 2025 has been designated by UNESCO as the International Year of Quantum Science and Technology. One hundred and twenty-five years ago, Max Planck's discovery of radiation quanta started the quantum era, and 100 years ago, quantum mechanics was developed by Schrödinger, Heisenberg, Bohr, Pauli, Dirac, Born, Fermi, and many others. By now, quantum mechanics is the theoretical foundation of most fields of physics and chemistry, and it is the basis for modern nanotechnology. How about plasma physics? How important are quantum effects in plasmas? In what experiments are quantum effects observed, and where do they govern the behavior of plasmas? How can these effects be treated theoretically and via computer simulations? Starting with a brief historical overview, we discuss the broad parameter range that is the characteristic of plasmas and outline where quantum effects are relevant. This is the case primarily for warm dense matter and inertial fusion plasmas. We provide an overview of the theoretical quantum methods that are available for these dense plasmas and how their respective advantages can be combined in order to achieve predictive capability. The key is a downfolding approach that is based on first-principles simulations.

We present extensive ab initio path integral Monte Carlo (PIMC) simulations of the two‐dimensional uniform electron gas (2DEG), covering a broad range of density parameters and temperatures . This allows us to analyze various structural, linear density response and spectral properties. We find clear evidence of a roton‐type feature in the dynamic structure factor at strong coupling and intermediate wavenumbers. We also benchmark novel dielectric theory implementations for the 2DEG [Kalkavouras et al. arXiv:2601.14989] for structural and spectral properties across the liquid phase diagram. The PIMC results can be used to benchmark existing theories and approximations, and guide the development of new methodologies.

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, we present “x-ray diagnostics, analysis, verification, and exploration”, a code designed to quickly estimate DSFs using the Chihara decomposition and analyze experimental spectra. The code is validated by re-analyzing 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. Finally, 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 experiments at the National Ignition Facility, similar to previously published results.

We present density response estimators for Monte Carlo simulations that are based on a reweighting procedure, where the samples of an unperturbed multi-component system are used to estimate the properties of a system perturbed by an external harmonic potential. This allows the species-resolved 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 generalized 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 wavenumber 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.

Recent advances in X-ray free-electron laser diagnostics have enabled direct probing of electronic properties 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 describing the electronic density and the electron–ion structure factor. Overcoming this limitation, we present a non-empirical KS-assisted orbital-free density functional framework for calculations under 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 of the order of 100 eV, quantum nonlocality remains essential for correctly describing the electron–ion structure factor in dense hydrogen.

Warm dense matter (WDM) is now routinely created and probed in laboratories around the world, providing unprecedented insights into conditions achieved in stellar atmospheres, planetary interiors, and inertial confinement fusion experiments. However, the interpretation of these experiments is often filtered through models with systematic errors that are difficult to quantify. Due to the simultaneous presence of quantum degeneracy and thermal excitation, transitions in which free electrons are de‐excited into thermally unoccupied bound states transferring momentum and energy to a scattered x‐ray photon become viable. Here we show that such free‐bound transitions are a particular feature of WDM and vanish in the limits of cold and hot temperatures. The inclusion of these transitions into the analysis of recent X‐ray Thomson Scattering experiments on WDM at the National Ignition Facility and the Linac Coherent Light Source is required to obtain a physically consistent temperature from the Chihara decomposition. This interpretation is corroborated by agreement with a recently developed model‐free thermometry technique and presents an important step for precisely characterizing and understanding the complex WDM state of matter.

We investigate basic hydrogen quantities like the molecular bond length, the molecular dissociation energy, and the van der Waals interaction in idealized situations in an effort to discern a suitable exchange-correlation functional for the molecular to metal transition in warm dense hydrogen. The best reproduction of bond length and dissociation energy is given by the r2SCAN functional. Several van der Waals functionals and also HSE06 fare qualitatively and quantitatively no better than Perdew–Burke–Ernzerhof or worse. r2SCAN however fails at reproducing the van der Waals energy minimum. In addition, we investigate quantities like the static and dynamic ion structure factor, and the electronic DOS to determine differences between exchange-correlation functionals with and without van der Waals corrections in the transition region from the molecular to the metallic regime of hydrogen.

This roadmap presents the state-of-the-art, current challenges and near future developments anticipated in the thriving field of warm dense matter (WDM) physics. Originating from strongly coupled plasma physics, high pressure physics and high energy density science, the WDM physics community has recently taken a giant leap forward. This is due to spectacular developments in laser technology, diagnostic capabilities, and computer simulation techniques. Only in the last decade has it become possible to perform accurate enough simulations & experiments to truly verify theoretical results as well as to reliably design experiments based on predictions. Consequently, this roadmap discusses recent developments of and contemporary challenges for theoretical methods and experimental techniques needed to describe, create and diagnose WDM. A large part of this roadmap is dedicated to specific WDM systems and applications in astrophysics, inertial confinement fusion and novel material synthesis.