Researchers use random numbers to accurately describe hot, dense hydrogen found inside some planets

Discovering the properties of quantum systems made up of many interacting particles remains a major challenge. Although the underlying mathematical equations have been known for a long time, they are too complex to be solved in practice. Breaking this barrier would most likely lead to a plethora of new discoveries and applications in physics, chemistry, and materials science.

Researchers at the Center for Advanced Systems Understanding (CASUS) at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) have now taken a big step forward by describing what is known as hot dense hydrogen – hydrogen under extremes like high pressure – more accurate than ever. . Their work is published in Physical examination letters.

The scientists’ approach, based on a method that uses random numbers, can for the first time solve the fundamental quantum dynamics of electrons involved when many hydrogen atoms interact under conditions found, for example, inside planets or in fusion reactors.

Hydrogen is the most abundant element in the universe. It’s the fuel that powers stars, including our sun, and it makes up the interiors of planets such as our solar system’s gas giant, Jupiter. The most common form of hydrogen in the universe is not the colorless, odorless gas, nor the hydrogen-containing molecules like water that are well known on Earth.

It is the hot, dense hydrogen of stars and planets – extremely compressed hydrogen – which in some cases conducts electricity like metals do. Hot dense matter research focuses on matter under conditions such as very high temperatures or pressures that are commonly found anywhere in the universe except the Earth’s surface where they do not exist. not naturally occur.

Simulation methods and their limits

In trying to elucidate the characteristics of hydrogen and other matter under extreme conditions, scientists rely heavily on simulations. A widely used theory is called density functional theory (DFT). Despite his success, he failed to describe hot, dense hydrogen. The main reason is that accurate simulations require precise knowledge of the interaction of electrons in hot, dense hydrogen.

But this knowledge is lacking and scientists still have to rely on approximations of this interaction, leading to inaccurate simulation results. Due to this lack of knowledge, it is not possible, for example, to accurately simulate the heating phase of inertial confinement fusion (ICF) reactions. Removing this hurdle could significantly advance ICF, one of the two main branches of fusion energy research, to become a relevant carbon-free power generation technology in the future.

In the new publication, lead author Maximilian Böhme, Dr. Zhandos Moldabekov, leader of the group of young researchers Dr. Tobias Dornheim (all CASUS-HZDR) and Dr. Jan Vorberger (Institute of Radiation Physics-HZDR) show for the first time that the properties of hot and dense hydrogen can be described very precisely with so-called Quantum Monte Carlo (QMC) simulations.

“What we’ve done is extend a QMC method called Path Integral Monte-Carlo (PIMC) to simulate the static electron density response of hot, dense hydrogen,” says Böhme, who is pursuing a Ph.D. with his work at CASUS. “Our method does not rely on the approximations that previous approaches have suffered from. Instead, it directly computes the fundamental quantum dynamics and is therefore very accurate. Regarding scale, however, our approach has its limitations because it is computationally intense. [we are] relying on the largest supercomputers, we can so far only manage particle numbers in the double-digit range.”

Higher and always precise scales

The implications of the new method could be far-reaching: intelligently combining PIMC and DFT could lead to advantages in both the accuracy of the PIMC method and the speed and versatility of the DFT method, the latter being much less intense in terms of Calculation.

“Until now, scientists have been digging through the fog to find reliable approximations of electronic correlations in their DFT simulations,” says Dornheim. “Using the PIMC results for very few particles as a reference, they can now adjust the parameters of their DFT simulations until the DFT results match the PIMC results. With the improved DFT simulations, we should be able to produce exact results in systems of hundreds to even thousands of particles.”

By adapting this approach, scientists could significantly improve DFT, which will result in improved simulations of the behavior of any type of matter or material. In fundamental research, it will enable predictive simulations that experimental physicists must compare with their experimental results from large-scale infrastructures such as the European X-Ray Free-Electron Laser Facility (European XFEL) near Hamburg (Germany), the Linac Coherent Light Source (LCLS) at the National Accelerator Laboratory in Menlo Park, or the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory in Livermore (both in the United States).

With respect to hydrogen, the work of Böhme and his colleagues could potentially help clarify the details of how hot, dense hydrogen becomes metallic hydrogen, a new phase of hydrogen that has been extensively studied. intensive both through experiments and simulations. The experimental generation of metallic hydrogen in the laboratory could allow interesting applications in the future.