Kiel physicists can precisely describe the behaviour of electrons under extreme conditions for the first time
Electrons are an elementary component of our world: they surround the core of all atoms, are essential to the formation of molecules, and primarily determine the properties of solids and liquids. They are also the charge carriers of electrical current, without which our high-tech environment with smartphones, computers and even the traditional light bulb would not be conceivable. In spite of their omnipresence in everyday life, we have not yet been able to accurately describe the behaviour of interacting electrons - only approximate it in models - especially at extreme temperatures and densities, such as inside planets or in stars. These are precisely the conditions of interest for a team of physics researchers from Kiel University (CAU). In collaboration with researchers from the USA and Great Britain, they have succeeded in describing the behaviour of electrons under these extreme conditions by means of accurate simulations. The scientists have thereby solved a problem that has confronted physics for decades. Their research findings are published in the current edition of the journal Physical Review Letters.
How electrons behave on a “large scale” - for example the relation between electrical voltage, resistance and current - is often easy to describe. However, on a microscopic level their behaviour is subject to the laws of quantum mechanics, which requires solving complex mathematical equations. The uniform electron gas is of particular physical significance in this context. It is not a gas in the literal sense, but rather a scientific model that describes important characteristics of electrons. Amongst other things, the electron gas is important to understand phenomena such as superconductivity, i.e. electrical current flow without resistance, or conduction electrons in solids. In addition, the model is the basis for the so-called density functional theory. The latter is currently the most widely-used simulation method in physics and chemistry, and is also used for investigating material properties in industry.
In the past, electron gas simulations were limited to electrons at very low temperature. In recent times, however, there has been growing interest in matter under extreme conditions - ten thousand times warmer than room temperature and up to a hundred times denser than conventional solids. "Accurately describing the behaviour of electrons at elevated temperatures is a previously-unsolved problem, which science has focussed on for decades," said Professor Michael Bonitz, professor of theoretical physics and head of the Kiel research team. In nature, this “warm dense matter” occurs inside planets, as well as in the Earth’s core, amongst other places. It can also be created experimentally in a laboratory, for example by targeted shooting of solid matter with a high-intensity laser, or with a free electron laser such as the new European XFEL in Hamburg. Warm dense matter is also relevant for inertial confinement fusion, which could provide a virtually unlimited source of clean energy in the future.
In order to describe the behaviour of electrons in the range of warm dense matter, the Kiel physicists combined new simulation methods that were developed at the CAU. Earlier results were based on various models, some of which contained approximations that are difficult to verify. However, using sophisticated computer simulations, the Kiel physicists were able to precisely solve the complex equations that describe the electron gas. In cooperation with colleagues from the Los Alamos National Laboratory (USA) and Imperial College London, the researchers thereby achieved the first complete and final description of the thermodynamic properties of interacting electrons in the range of warm dense matter. "These results are the first exact data in this area, and will take our understanding of matter at extreme temperatures to a new level," explained Bonitz. "Amongst other things, now the partly 40-year-old existing models can be reviewed and improved for the first time. We have already been able to prove deviations of 10 to 15 percent." At the end of the Kiel-based scientists’ years of hard work, they now have extensive data sets and formulas which they hope will be important for comparison with experiments, and will provide input into further theories, thus also helping other scientists in their research.
Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions, Simon Groth, Tobias Dornheim, Travis Sjostrom, Fionn D. Malone, W.M.C. Foulkes, and Michael Bonitz
Physical Review Letters 119, 135001, DOI: 10.1103/PhysRevLett.119.135001, journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.135001
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The Kiel physicists Tobias Dornheim, Simon Groth and Professor Michael Bonitz have developed a simulation procedure, with which the properties of electrons at extreme temperatures can be calculated exactly for the first time.
Photo: Julia Siekmann
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In nature, the hot, dense matter of electron gas occurs inside planets, such as here in Jupiter. On Earth, they can only be created in a laboratory, for example with a free electron laser such as at the European XFEL in Hamburg.
Photo: NASA/JPL-Caltech/SwRI/MSSS/Gabriel Fiset
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Professor Michael Bonitz
Institute of Theoretical Physics and Astrophysics,
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