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Category: mathematics

Quantum gas resists heating under periodic kicks, revealing many-body localization mechanism

A joint theoretical study by the University of Innsbruck and Zhejiang University has uncovered the microscopic origin of a striking quantum phenomenon: a periodically driven gas of ultracold atoms that simply refuses to heat up, defying classical expectations.

Push a swing repeatedly in rhythm, and it swings higher and higher, absorbing more and more energy. A quantum gas, however, can behave very differently. Under periodic kicks, quantum interference can freeze energy absorption entirely, a phenomenon known as dynamical localization. Whether this survives when particles interact with each other has been a long-standing open question. A 2025 experiment by the research group of Hanns-Christoph Nägerl at the Department of Experimental Physics confirmed that it can. But the microscopic reasons remained until now unclear.

A new theoretical study by Prof. Lei Ying’s team at Zhejiang University, in collaboration with Prof. Hanns-Christoph Nägerl’s group at the University of Innsbruck, published in Physical Review Letters, provides the missing explanation. The team developed a mathematical framework that transforms the complex-driven many-body problem into a tractable lattice model. This reveals that interactions introduce a universal power-law structure that reshapes localization—and ultimately drives its breakdown at intermediate interaction strengths.

Single mathematical model helps solve a decades-old puzzle involving ultrafast lasers

A team of international researchers, including an Aston University researcher, has cracked the code on how “breather” laser pulses work, creating a single mathematical model that explains two completely different laser behaviors for the first time. Ultrafast lasers emit extremely short pulses of light, lasting only picoseconds or femtoseconds, making them essential for applications ranging from eye surgery and biomedical imaging to precision materials processing and advanced manufacturing.

The work is published in the journal Physical Review Letters. By understanding laser behaviors better, scientists will be able to control them, making lasers more reliable and better suited to specific applications.

An ultrafast laser produces pulses of light that circulate within the laser cavity, where they can evolve into stable structures called solitons. Solitons tend to maintain their shape as they travel, unlike conventional light pulses which spread out. Usually, these solitons are identical and regular, like a heartbeat, known as steady-state emission. In a “breather” laser, the solitons change over time and successive cavity round trips, growing and shrinking before repeating the cycle, like a breathing pattern. This is an example of a non-equilibrium state, where the laser output does not remain constant but keeps evolving over time.

Could the mathematical ‘shape’ of the universe solve the cosmological constant problem?

The cosmological constant is the mathematical description of the energy that drives the ever-accelerating expansion of the cosmos. It’s also the source of one of the most enduring and confounding problems in modern physics.

The constant’s observed value is fundamentally at odds with quantum field theory (QFT), the leading theory describing the elementary particles and forces that make up the universe. QFT predicts that quantum fluctuations in the vacuum of space should make the value of the constant enormous—practically infinite. But its observed value is a tiny fraction of that prediction.

Researchers at Brown University have proposed a provocative new answer for why that is.

I’ve fired one of America’s most powerful lasers—here’s what a shot day looks like

If you walk across the open yard in front of the Physics, Math and Astronomy building at the University of Texas at Austin, you’ll see a 17-story tower and a huge L-shaped building. What you won’t see is what’s underneath you. Two floors below ground, behind heavy double doors stamped with a logo that most students have never noticed, sits one of the most powerful lasers in the United States.

I was the lead laser scientist on the Texas Petawatt, or TPW as we called it, from 2020 to 2024. Texas Petawatt, which is currently closed due to funding cuts, was a government-funded research center where scientists from across the country applied for time to use specialized equipment. It was part of LaserNetUS, a Department of Energy network of high-power laser labs.

This type of laser takes a tiny pulse of light, stretches it out so it doesn’t blast optics to pieces, and amplifies it until, for a brief instant, it carries more power than the entire U.S. electrical grid. Then it compresses the pulse back to a trillionth of a second to create a star in a vacuum chamber.

World’s largest collection of Olympiad-level math problems now available to everyone

Every year, the countries competing in the International Mathematical Olympiad arrive with a booklet of their best, most original problems. Those booklets get shared among delegations, then quietly disappear. No one had ever collected them systematically, cleaned them, and made them available—not for AI researchers testing the limits of mathematical reasoning, and not for the students around the world training for these competitions largely on their own.

Researchers at MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL), King Abdullah University of Science and Technology (KAUST), and HUMAIN have now done exactly that.

MathNet is the largest high-quality dataset of proof-based math problems ever created, and it is not closed. Comprising more than 30,000 expert-authored problems and solutions spanning 47 countries, 17 languages, and 143 competitions, it is five times larger than the next biggest dataset of its kind. The work will be presented at the International Conference on Learning Representations (ICLR 2026) in Brazil later this month.

Long-Term Cognitive Ability and Academic Achievement After Childhood Severe Malaria

Among children with a history of CerebralMalaria or severe malarial anemia, long-term follow-up demonstrated lower overall cognitive ability and lower math achievement compared with unaffected children when assessed 4 to 15 years after the index episode of Malaria.

Attention and reading scores did not differ, and outcomes among children with other forms of severe malaria were similar to unaffected children.

These findings indicate that specific severe malaria phenotypes are associated with persistent cognitive and academic effects into later childhood and adolescence, with implications for long-term follow-up and supportive services.

ESCMIDGlobal2026.

This descriptive analysis uses a subset of data from the Malarial Impact on Neurobehavioral Development (MIND) cohort study to assess whether severe malaria in Ugandan children is associated with long-term cognitive impairment or decreased academic achievement.

The Theory Of Everything That Nobody Talks About

Learn more about physics and mathematics on Brilliant! Get your first 30 days free as well as 20% off an annual premium subscription when you use my link ➜ https://brilliant.org/sabine.

There are a whole lot of people with “theories of everything” – theories which supposedly explain how the whole universe works. Most of the time, these theories fall very short of that goal. Causal Fermion Systems are an approach that actually seems promising… though it still has its flaws. Today I have a brief summary of what might be the most underreported theory of everything out there.

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New methods can help study the phenomenon of turbulence

In his doctoral thesis, Michael Roop develops numerical methods that allow finding physically reliable approximate solutions to nonlinear differential equations used to model turbulence.

Many processes in nature can be described by differential equations, but only a few of them can be solved explicitly with solutions in formulas. This is the motivation for developing numerical equations to find approximate solutions. The numerical equations developed in Roop’s thesis have a particular focus on geometric properties. Though the thesis is mathematical, the problems it addresses originate in physics and mainly have to do with magnetohydrodynamic (MHD) turbulence.

“It is difficult to define turbulence rigorously. Intuitively, you can think of the turbulent behavior when a fluid moves, but it is very hard to predict how it will behave in the future. It looks chaotic though there is no randomness in the models of motion.”

Stephen Hawking’s black hole information paradox could be solved — if the universe has 7 dimensions

The new research explores a universe with more dimensions than the familiar four. In this framework, the cosmos contains seven dimensions, three of which are compact and invisible at everyday scales.

“We experience three dimensions of space and one of time — four dimensions in total,” Pinčák said. “Our model proposes that the universe actually has seven dimensions: the four we know, plus three tiny extra dimensions curled up so tightly that we cannot directly perceive them.”

These extra dimensions are arranged in a highly symmetrical structure known as a G₂ geometry. This mathematical framework, often explored in advanced theories such as a version of string theory known as M-theory, determines how the hidden dimensions are “folded.”

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