Researchers use random numbers to accurately describe the dense, warm hydrogen found in some of the inner planets

Roll the dice to gain insight into the planets and stars

The stars of the universe laid on Earth (photomontage): The Helmholtz International beamline of extreme fields is used to create warm dense matter in the laboratory for the study of celestial bodies. Now, physicists can make reliable predictions for future experiments. Credit: HZDR/Science Communication Lab

Discovering the properties of quantum systems composed of many interacting particles remains a major challenge. While the basic mathematical equations have been known for a long time, they are far too complex to solve in practice. Breaking this barrier will 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) in Helmholtz-Zentrum Dresden-Rossendorf (HZDR) have now taken a huge step forward by describing a so-called warm density. hydrogenunder hydrogen extreme conditions Like high pressures – with more precision than ever before. Their work has been published in Physical review letters.

Scholars’ method-based approaches lay out random numbers To use it, they can for the first time solve the fundamental quantum dynamics of the electrons involved when they are many hydrogen atoms They interact under conditions that exist, for example, in the interiors of planets or fusion reactors.

Hydrogen is the most abundant element in the universe. It’s the fuel that powers stars including our sun, and makes up the interior of planets like the gas giant Jupiter of our solar system. The most common form of hydrogen in the universe is neither the colorless, odorless gas, nor hydrogen-containing molecules such as water known on Earth.

It’s the dense, warm hydrogen of stars and planets – highly compressed hydrogen – that in some cases conducts electricity like metals. Warm dense matter research focuses on matter under conditions such as extremely high temperatures or pressures that are commonly found everywhere in the universe except on Earth’s surface where it does not occur naturally.

Simulation methods and their limitations

In an effort to elucidate the properties of hydrogen and other materials under extreme conditions, scientists rely heavily on simulations. One widely used is called Density functional theory (DFT). Although successful, it fails to describe warm, dense hydrogen. The main reason is that accurate simulations require accurate knowledge of the interaction of electrons in warm, dense hydrogen.

But this knowledge is missing, and scientists still have to rely on rough estimates of this interaction, which leads to inaccuracies simulation Results. Because of this knowledge gap, it is not possible, for example, to accurately simulate the heating phase of self-confinement fusion (ICF) reactions. Removing this barrier could significantly advance ICF, one of two major branches of fusion energy research, into becoming a relevant technology for carbon-neutral power generation in the future.

In the new publication, lead author Maximilian Böhme, Dr Zhandos Moldabekov, Young Investigator Group Leader Dr Tobias Dornheim (all CASUS-HZDR), and Dr Jan Vorberger (Institute for Radiation Physics-HZDR) show for the first time that properties of warm dense hydrogen can be described very precisely. Using what is called a Quantum Monte Carlo (QMC) simulation.

“What we’ve done is extend a QMC method called Path Integral Monte Carlo (PIMC) to simulate the constant electronic density response of warm dense hydrogen,” says Boehm, who is pursuing his doctorate on his work at CASUS. “Our method does not rely on approximations that previous approaches have suffered from. Instead, it computes fundamental quantum dynamics directly and is therefore very precise. And when it comes to scale, our approach has its limitations because it is computationally intensive. [we are] Relying on the largest supercomputers, we can so far only deal with numbers of particles in the two-digit range. “

Higher gauges – and still accurate

The implications of the new method could be far-reaching: cleverly combining PIMC and DFT could yield benefits from the accuracy of the PIMC method and the speed and versatility of the DFT method—the latter method being less computationally intensive.

“Until now, scientists have been searching through the haze to find reliable approximations of the electronic correlations in their DFT simulations,” says Dornheim. “Using the PIMC results for a very small number of particles as a reference, they can now adjust their DFT simulation settings so that the DFT results match the PIMC results. With improved DFT simulations, we should be able to achieve accurate results in systems of hundreds to even thousands of particles.”

By adapting this approach, scientists can greatly enhance DFT, which will result in improved simulations of the behavior of any type of material or material. in Basic researchit will allow predictive simulation experimental physicists need to compare their experimental results from large-scale infrastructures such as the 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 the Lawrence Livermore National Laboratory in Livermore (both in the US).

With regard to hydrogen, Boehm and colleagues’ work could help elucidate the details of how dense, warm hydrogen turns into metallic hydrogen, a new phase of hydrogen that has been intensively studied through experiments and simulations. Generating metallic hydrogen experimentally in the laboratory could enable interesting applications in the future.

more information:
Maximilian Böhme et al, Constant Electronic Density Response to Warm Dense Hydrogen: An Ab Initio Path Integral Monte Carlo Simulation, Physical review letters (2022). DOI: 10.1103/PhysRevLett.129.066402

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