Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions

Behaviour of electrons underextreme conditions described for the first time 

A group of researchers including TYC Professor Matthew Foulkes from Imperial College have modelled the actions of electrons under extreme temperatures and densities, such as found within planets and stars.

The work could provide insights into the behaviour of matter in inertial confinement fusion experiments, which may one day lead to a sought-after source of clean energy.

Electrons are an elementary component of our world and determine many of 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 large numbers of interacting electrons, especially at extreme temperatures and densities, such as inside planets or in stars. We have plenty of approximate models to choose from, but little idea of their accuracy or reliability.

Now, a research team comprising groups from Kiel University, Imperial College London, Los Alamos, and the Lawrence Livermore National Laboratory has succeeded in describing 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 will appear today 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. On a microscopic level, however, the electrons in liquids and solids behave like a quantum mechanical gas, which can only be understood by solving the complicated mathematical equations of quantum theory.

Theories of the electron gas underlie our understanding of the electrical properties of solids, including superconductivity - electrical current flow without resistance. They also underpin the so-called density functional theory, the most widely used simulation method in physics and chemistry, which is used for investigating material properties in industry.

In the past, simulations were only able to describe the electron gas 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.

Professor Michael Bonitz, professor of theoretical physics and head of the Kiel research team, said: "Accurately describing the behaviour of electrons at elevated temperatures is a previously-unsolved problem, which science has focussed on for decades.”

In nature, this “warm dense matter” occurs inside planets, including the Earth’s core. 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.

Earlier theories of warm dense matter behaviour were based on models based on approximations that are difficult to verify. However, using sophisticated computer simulations, the physicists were able to precisely solve the complex equations that describe the electron gas.

The team thereby achieved the first complete and final description of the thermodynamic properties of interacting electrons in the range of warm dense matter. Professor Bonitz said: "These results are the first exact data in this area, and will take our understanding of matter at extreme temperatures to a new level."

"Amongst other things, the 40-year-old existing models can now be reviewed and improved for the first time. We have already been able to prove deviations of 10 to 15 percent."

The team hope the extensive data sets and formulas built up in the project will be important for comparison with experiments and will provide input into further theories, helping other scientists in their research. As Professor Matthew Foulkes of Imperial College says: “It took five years and a team of scientists from three countries to develop the new techniques necessary to describe warm dense matter accurately. Now, at last, we are in a position to carry out accurate and direct simulations of planetary interiors, solids under intense laser irradiation, laser-activated catalysts, and other warm dense systems. This is the beginning of a new field of computational science.”

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.135001

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