This workshop serves as a platform to discuss methods of density functional theory (DFT) that are used to study the behavior of matter under extreme conditions as found in planets and stars.
Ronald Redmer
Attila Cangi
DFT-MD
Invited lecture
Invited talk
The detection of more than 4000 exoplanets, most of them having no equivalent in the Solar Systems, stimulates numerous fields of research in order to better understand the structure, the formation, the evolution and the habitability of these new worlds. In order to build realistic models, astrophysicists are in need for the physical properties (equations of state, phase diagrams, transport properties,…) of various materials on a wide range of thermodynamic conditions. In this regard, ab initio numerical simulations have proven to be a wonderful tool to accurately characterize the properties of matter under extreme conditions. These advances lead to paradigm shifts regarding the structure of planets, such as Jupiter’s core erosion for instance or the origin of Super-Earth magnetic field. In this presentation, I will show on a few examples how the concurrent use of ab initio simulations and laser experiments can help to better comprehend exoplanets as well as to provide constraints on the selection of priority targets for followup observations.
The determination of thermoelectric transport coefficients of dense, partially ionized plasmas is a great challenge for both experiment and theory. In the past two decades, density functional theory (DFT) has evolved to an efficient tool for making theoretical predictions of properties of dense plasmas. Many of these are of high relevance for modelling the interior states, evolution, and magnetic field dynamics of stellar and planetary objects.
Here I will give an overview on the generalized Kubo-Greenwood formalism [1] that is frequently used in calculations of electronic transport properties using the Kohn-Sham states from DFT. Several examples for successful application of this technique to various solid and fluid metals will be presented. Furthermore, a comparison of optical reflectivities of molecular fluids with shock compression experiments [2] will be made.
Finally, the limits of the Kubo-Greenwood formalism with respect to its capability of describing electron-electron collisions will be discussed by comparing the thermopower and Lorenz number of weakly degenerate hydrogen plasmas with the known Spitzer results.
This work is supported by the DFG within the FOR 2440 "Matter under Planetary Interior
Conditions - High Pressure, Planetary, and Plasma Physics."
REFERENCES
[1] B. Holst, M. French and R. Redmer, "Electronic transport coefficients from ab initio simulations and application to dense liquid hydrogen", Phys. Rev. B 83, 235120 (2011).
[2] A. Ravasio, M. Bethkenhagen, J.-A. Hernandez, A. Benuzzi-Mounaix, F. Datchi, M. French, M. Guarguaglini, F. Lefevre, S. Ninet, R. Redmer, and T. Vinci, "Metallization of Shock-Compressed Liquid Ammonia", Phys. Rev. Lett. 126, 025003 (2019).
Stochastic DFT, DFT-MD, and related
Invited lecture
Invited talk
Invited talk
Warm dense matter is of high current interest for many applications, including astrophysics, material science, and fusion research. Yet, the accurate description of electronic correlation effects at these conditions is most difficult, and often computationally intensive ab-initio methods have to be used [1]. The most accurate approach is given by the quantum Monte Carlo (QMC) technique, which is, in principle, capable to give one exact results for the full quantum many-body problem of interest without any empirical input. Consequently, parametrizations of accurate QMC data constitute the basis for a gamut of applications, such as the construction of XC-functionals for density functional theory (DFT).
In this talk, I focus on the electronic density response of WDM to an external perturbation, which is of central interest for WDM theory, such as the interpretation of X-ray Thomson scattering (XRTS) experiments and the construction of advanced XC-functionals for DFT. In particular, I will show how we can use the ab-initio path integral Monte Carlo (PIMC) method to estimate the exact density response to an external harmonic perturbation. First and foremost, this allows us to compute the electronic XC-kernel (also known as local field correction in the context of dielectric theory), which has recently become available as a neural-net representation [2] for a uniform electron gas. Secondly, I will show how our imaginary-time PIMC data can be used as a starting point for an analytic continuation [3]. This gives us access to the dynamic structure factor, which is the key property in XRTS experiments. Lastly, I will talk about nonlinear effects in WDM [4], which cannot be neglected in many situations of experimental relevance.
[1] M. Bonitz, T. Dornheim, Z.A. Moldabekov, S. Zhang, P. Hamann, H. Kählert, A. Filinov, K. Ramakrishna, and J. Vorberger, Phys. Plasmas 27, 042710 (2020)
[2] T. Dornheim, J. Vorberger, S. Groth, N. Hoffmann, Z. Moldabekov, and M. Bonitz, J. Chem. Phys. 151, 194104 (2019)
[3] T. Dornheim, S. Groth, J. Vorberger, and M. Bonitz, Phys. Rev. Lett. 121, 255001 (2018)
[4] T. Dornheim, J. Vorberger, and M. Bonitz, Phys. Rev. Lett. 125, 085001 (2020)
Invited talk
The successful characterization of high energy density (HED) phenomena in laboratories using pulsed power facilities and coherent light sources is possible only with numerical modeling for design, diagnostic development, and data interpretation. The persistence of electron correlation in HED matter is one of the greatest challenges for accurate numerical modeling and has hitherto impeded our ability to model HED phenomena across multiple length and time scales at sufficient accuracy. Standard methods from electronic structure theory capture electron correlation at high accuracy, but are limited to small scales due to their high computational cost. In this talk, I will summarize our recent efforts on devising a data-driven and physics-informed workflow to tackle this challenge [1]. Based on first-principles data we generate machine-learning surrogate models that replace traditional density functional theory calculations. Our surrogates predict the electronic structure and related properties of matter under extreme conditions highly efficiently while maintaining the accuracy of traditional methods.
[1] J. A. Ellis, L. Fiedler, G. A. Popoola, N. A. Modine, J. A. Stephens, A. P. Thompson, A. Cangi, and S. Rajamanickam, Phys. Rev. B 104, 035120 (2021).
Invited talk
Invited talk
Libxc, one of a few available libraries for exchange-correlation functionals, currently contains well above 100 different LDA, GGA, hybrid GGA, meta-GGA, and hybrid meta-GGA functionals. The aim of this talk is to show the results of trying quite a few of these for different warm dense matter states and different properties. When possible, quantum Monte Carlo data will be used to benchmark the DFT results.
Invited lecture
Invited talk
The simulation of correlated fermions is important for various phenomena in warm dense matter, plasmonics, and ultracold atoms. In order to enable simulations at larger length and longer time scales, there is a need to develop quantum hydrodynamics (QHD) as a complementary method to commonly used first-principles methods. The key difference of the QHD from classical fluid equations is the inclusion of the quantum non-locality. This is usually done by using the Bohm potential. We performed the very first investigation of the Bohm potential for a correlated many-fermion system based on the data from KS-DFT. Despite its long history in quantum mechanics since its derivation by Bohm in 1952 and its importance for QHD, this has not been done before. Our key result shows the very limited applicability of the standard Bohm potential which is used in virtually all previous works of QHD. We showed that it is only valid for a very weakly perturbed electron gas. We illustrate that the many-fermion quantum Bohm potential is needed to model nonlinear phenomena in quantum plasmas and WDM [1, 2].
[1] Z. A. Moldabekov, T. Dornheim, G. Gregori, F. Graziani, M. Bonitz, A. Cangi, Towards a Quantum Fluid Theory of Correlated Many-Fermion Systems from First Principles, SciPost Physics [accepted for publication], scipost_202106_00020v3
[2] F. Graziani, Z. Moldabekov, B. Olson, M. Bonitz, Shock Physics in Warm Dense Matter--a quantum hydrodynamics perspective, arXiv:2109.09081
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