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Wavefunction matching for solving quantum many-body problems

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Wavefunction matching for solving quantum many-body problems


Strongly interacting systems play an important role in quantum physics and quantum chemistry. Stochastic methods such as Monte Carlo simulations are a proven method for investigating such systems. However, these methods reach their limits when so-called sign oscillations occur. This problem has now been solved by an international team of researchers from Germany, Turkey, the USA, China, South Korea and France using the new method of wavefunction matching. As an example, the masses and radii of all nuclei up to mass number 50 were calculated using this method. The results agree with the measurements, the researchers now report in the journal “Nature.”

All matter on Earth consists of tiny particles known as atoms. Each atom contains even smaller particles: protons, neutrons and electrons. Each of these particles follows the rules of quantum mechanics. Quantum mechanics forms the basis of quantum many-body theory, which describes systems with many particles, such as atomic nuclei.

One class of methods used by nuclear physicists to study atomic nuclei is the ab initio approach. It describes complex systems by starting from a description of their elementary components and their interactions. In the case of nuclear physics, the elementary components are protons and neutrons. Some key questions that ab initio calculations can help answer are the binding energies and properties of atomic nuclei and the link between nuclear structure and the underlying interactions between protons and neutrons.

However, these ab initio methods have difficulties in performing reliable calculations for systems with complex interactions. One of these methods is quantum Monte Carlo simulations. Here, quantities are calculated using random or stochastic processes. Although quantum Monte Carlo simulations can be efficient and powerful, they have a significant weakness: the sign problem. It arises in processes with positive and negative weights, which cancel each other. This cancellation leads to inaccurate final predictions.

A new approach, known as wavefunction matching, is intended to help solve such calculation problems for ab initio methods. “This problem is solved by the new method of wavefunction matching by mapping the complicated problem in a first approximation to a simple model system that does not have such sign oscillations and then treating the differences in perturbation theory,” says Prof. Ulf-G. Meißner from the Helmholtz Institute for Radiation and Nuclear Physics at the University of Bonn and from the Institute of Nuclear Physics and the Center for Advanced Simulation and Analytics at Forschungszentrum Jülich. “As an example, the masses and radii of all nuclei up to mass number 50 were calculated — and the results agree with the measurements,” reports Meißner, who is also a member of the Transdisciplinary Research Areas “Modeling” and “Matter” at the University of Bonn.

“In quantum many-body theory, we are often faced with the situation that we can perform calculations using a simple approximate interaction, but realistic high-fidelity interactions cause severe computational problems,” says Dean Lee, Professor of Physics from the Facility for Rare Istope Beams and Department of Physics and Astronomy (FRIB) at Michigan State University and head of the Department of Theoretical Nuclear Sciences.

Wavefunction matching solves this problem by removing the short-distance part of the high-fidelity interaction and replacing it with the short-distance part of an easily calculable interaction. This transformation is done in a way that preserves all the important properties of the original realistic interaction. Since the new wavefunctions are similar to those of the easily computable interaction, the researchers can now perform calculations with the easily computable interaction and apply a standard procedure for handling small corrections — called perturbation theory.

The research team applied this new method to lattice quantum Monte Carlo simulations for light nuclei, medium-mass nuclei, neutron matter and nuclear matter. Using precise ab initio calculations, the results closely matched real-world data on nuclear properties such as size, structure and binding energy. Calculations that were once impossible due to the sign problem can now be performed with wavefunction matching.

While the research team focused exclusively on quantum Monte Carlo simulations, wavefunction matching should be useful for many different ab initio approaches. “This method can be used in both classical computing and quantum computing, for example to better predict the properties of so-called topological materials, which are important for quantum computing,” says Meißner.

The first author is Prof. Dr. Serdar Elhatisari, who worked for two years as a Fellow in Prof. Meißner’s ERC Advanced Grant EXOTIC. According to Meißner, a large part of the work was carried out during this time. Part of the computing time on supercomputers at Forschungszentrum Jülich was provided by the IAS-4 institute, which Meißner heads.



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Early dark energy could resolve cosmology’s two biggest puzzles

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Wavefunction matching for solving quantum many-body problems


A new study by MIT physicists proposes that a mysterious force known as early dark energy could solve two of the biggest puzzles in cosmology and fill in some major gaps in our understanding of how the early universe evolved.

One puzzle in question is the “Hubble tension,” which refers to a mismatch in measurements of how fast the universe is expanding. The other involves observations of numerous early, bright galaxies that existed at a time when the early universe should have been much less populated.

Now, the MIT team has found that both puzzles could be resolved if the early universe had one extra, fleeting ingredient: early dark energy. Dark energy is an unknown form of energy that physicists suspect is driving the expansion of the universe today. Early dark energy is a similar, hypothetical phenomenon that may have made only a brief appearance, influencing the expansion of the universe in its first moments before disappearing entirely.

Some physicists have suspected that early dark energy could be the key to solving the Hubble tension, as the mysterious force could accelerate the early expansion of the universe by an amount that would resolve the measurement mismatch.

The MIT researchers have now found that early dark energy could also explain the baffling number of bright galaxies that astronomers have observed in the early universe. In their new study, reported in the Monthly Notices of the Royal Astronomical Society, the team modeled the formation of galaxies in the universe’s first few hundred million years. When they incorporated a dark energy component only in that earliest sliver of time, they found the number of galaxies that arose from the primordial environment bloomed to fit astronomers’ observations.

You have these two looming open-ended puzzles,” says study co-author Rohan Naidu, a postdoc in MIT’s Kavli Institute for Astrophysics and Space Research. “We find that in fact, early dark energy is a very elegant and sparse solution to two of the most pressing problems in cosmology.”

The study’s co-authors include lead author and Kavli postdoc Xuejian (Jacob) Shen, and MIT professor of physics Mark Vogelsberger, along with Michael Boylan-Kolchin at the University of Texas at Austin, and Sandro Tacchella at the University of Cambridge.

Big city lights

Based on standard cosmological and galaxy formation models, the universe should have taken its time spinning up the first galaxies. It would have taken billions of years for primordial gas to coalesce into galaxies as large and bright as the Milky Way.

But in 2023, NASA’s James Webb Space Telescope (JWST) made a startling observation. With an ability to peer farther back in time than any observatory to date, the telescope uncovered a surprising number of bright galaxies as large as the modern Milky Way within the first 500 million years, when the universe was just 3 percent of its current age.

“The bright galaxies that JWST saw would be like seeing a clustering of lights around big cities, whereas theory predicts something like the light around more rural settings like Yellowstone National Park,” Shen says. “And we don’t expect that clustering of light so early on.”

For physicists, the observations imply that there is either something fundamentally wrong with the physics underlying the models or a missing ingredient in the early universe that scientists have not accounted for. The MIT team explored the possibility of the latter, and whether the missing ingredient might be early dark energy.

Physicists have proposed that early dark energy is a sort of antigravitational force that is turned on only at very early times. This force would counteract gravity’s inward pull and accelerate the early expansion of the universe, in a way that would resolve the mismatch in measurements. Early dark energy, therefore, is considered the most likely solution to the Hubble tension.

Galaxy skeleton

The MIT team explored whether early dark energy could also be the key to explaining the unexpected population of large, bright galaxies detected by JWST. In their new study, the physicists considered how early dark energy might affect the early structure of the universe that gave rise to the first galaxies. They focused on the formation of dark matter halos — regions of space where gravity happens to be stronger, and where matter begins to accumulate.

“We believe that dark matter halos are the invisible skeleton of the universe,” Shen explains. “Dark matter structures form first, and then galaxies form within these structures. So, we expect the number of bright galaxies should be proportional to the number of big dark matter halos.”

The team developed an empirical framework for early galaxy formation, which predicts the number, luminosity, and size of galaxies that should form in the early universe, given some measures of “cosmological parameters.” Cosmological parameters are the basic ingredients, or mathematical terms, that describe the evolution of the universe.

Physicists have determined that there are at least six main cosmological parameters, one of which is the Hubble constant — a term that describes the universe’s rate of expansion. Other parameters describe density fluctuations in the primordial soup, immediately after the Big Bang, from which dark matter halos eventually form.

The MIT team reasoned that if early dark energy affects the universe’s early expansion rate, in a way that resolves the Hubble tension, then it could affect the balance of the other cosmological parameters, in a way that might increase the number of bright galaxies that appear at early times. To test their theory, they incorporated a model of early dark energy (the same one that happens to resolve the Hubble tension) into an empirical galaxy formation framework to see how the earliest dark matter structures evolve and give rise to the first galaxies.

“What we show is, the skeletal structure of the early universe is altered in a subtle way where the amplitude of fluctuations goes up, and you get bigger halos, and brighter galaxies that are in place at earlier times, more so than in our more vanilla models,” Naidu says. “It means things were more abundant, and more clustered in the early universe.”

“A priori, I would not have expected the abundance of JWST’s early bright galaxies to have anything to do with early dark energy, but their observation that EDE pushes cosmological parameters in a direction that boosts the early-galaxy abundance is interesting,” says Marc Kamionkowski, professor of theoretical physics at Johns Hopkins University, who was not involved with the study. “I think more work will need to be done to establish a link between early galaxies and EDE, but regardless of how things turn out, it’s a clever — and hopefully ultimately fruitful — thing to try.”

We demonstrated the potential of early dark energy as a unified solution to the two major issues faced by cosmology. This might be an evidence for its existence if the observational findings of JWST get further consolidated,” Vogelsberger concludes. “In the future, we can incorporate this into large cosmological simulations to see what detailed predictions we get.”

This research was supported, in part, by NASA and the National Science Foundation.



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Plant-derived secondary organic aerosols can act as mediators of plant-plant interactions

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Wavefunction matching for solving quantum many-body problems


A new study published in Science reveals that plant-derived secondary organic aerosols (SOAs) can act as mediators of plant-plant interactions. This research was conducted through the cooperation of chemical ecologists, plant ecophysiologists and atmospheric physicists at the University of Eastern Finland.

It is well known that plants release volatile organic compounds (VOCs) into the atmosphere when damaged by herbivores. These VOCs play a crucial role in plant-plant interactions, whereby undamaged plants may detect warning signals from their damaged neighbours and prepare their defences. “Reactive plant VOCs undergo oxidative chemical reactions, resulting in the formation of secondary organic aerosols (SOAs). We wondered whether the ecological functions mediated by VOCs persist after they are oxidated to form SOAs,” said Dr. Hao Yu, formerly a PhD student at UEF, but now at the University of Bern.

The study showed that Scots pine seedlings, when damaged by large pine weevils, release VOCs that activate defences in nearby plants of the same species. Interestingly, the biological activity persisted after VOCs were oxidized to form SOAs. The results indicated that the elemental composition and quantity of SOAs likely determines their biological functions.

“A key novelty of the study is the finding that plants adopt subtly different defence strategies when receiving signals as VOCs or as SOAs, yet they exhibit similar degrees of resistance to herbivore feeding,” said Professor James Blande, head of the Environmental Ecology Research Group. This observation opens up the possibility that plants have sophisticated sensing systems that enable them to tailor their defences to information derived from different types of chemical cue.

“Considering the formation rate of SOAs from their precursor VOCs, their longer lifetime compared to VOCs, and the atmospheric air mass transport, we expect that the ecologically effective distance for interactions mediated by SOAs is longer than that for plant interactions mediated by VOCs,” said Professor Annele Virtanen, head of the Aerosol Physics Research Group. This could be interpreted as plants being able to detect cues representing close versus distant threats from herbivores.

The study is expected to open up a whole new complex research area to environmental ecologists and their collaborators, which could lead to new insights on the chemical cues structuring interactions between plants.



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Folded or cut, this lithium-sulfur battery keeps going

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Wavefunction matching for solving quantum many-body problems


Most rechargeable batteries that power portable devices, such as toys, handheld vacuums and e-bikes, use lithium-ion technology. But these batteries can have short lifetimes and may catch fire when damaged. To address stability and safety issues, researchers reporting in ACS Energy Letters have designed a lithium-sulfur (Li-S) battery that features an improved iron sulfide cathode. One prototype remains highly stable over 300 charge-discharge cycles, and another provides power even after being folded or cut.

Sulfur has been suggested as a material for lithium-ion batteries because of its low cost and potential to hold more energy than lithium-metal oxides and other materials used in traditional ion-based versions. To make Li-S batteries stable at high temperatures, researchers have previously proposed using a carbonate-based electrolyte to separate the two electrodes (an iron sulfide cathode and a lithium metal-containing anode). However, as the sulfide in the cathode dissolves into the electrolyte, it forms an impenetrable precipitate, causing the cell to quickly lose capacity. Liping Wang and colleagues wondered if they could add a layer between the cathode and electrolyte to reduce this corrosion without reducing functionality and rechargeability.

The team coated iron sulfide cathodes in different polymers and found in initial electrochemical performance tests that polyacrylic acid (PAA) performed best, retaining the electrode’s discharge capacity after 300 charge-discharge cycles. Next, the researchers incorporated a PAA-coated iron sulfide cathode into a prototype battery design, which also included a carbonate-based electrolyte, a lithium metal foil as an ion source, and a graphite-based anode. They produced and then tested both pouch cell and coin cell battery prototypes.

After more than 100 charge-discharge cycles, Wang and colleagues observed no substantial capacity decay in the pouch cell. Additional experiments showed that the pouch cell still worked after being folded and cut in half. The coin cell retained 72% of its capacity after 300 charge-discharge cycles. They next applied the polymer coating to cathodes made from other metals, creating lithium-molybdenum and lithium-vanadium batteries. These cells also had stable capacity over 300 charge-discharge cycles. Overall, the results indicate that coated cathodes could produce not only safer Li-S batteries with long lifespans, but also efficient batteries with other metal sulfides, according to Wang’s team.

The authors acknowledge funding from the National Natural Science Foundation of China; the Natural Science Foundation of Sichuan, China; and the Beijing National Laboratory for Condensed Matter Physics.



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