Math Physics math.MP

In the 1920s, British meteorologist Gilbert Walker, trying to forecast monsoons in India, noticed a strange connection: when air pressure rises over the eastern Pacific, it falls over the western Pacific, and vice versa. It was as if a giant air pendulum were swinging along the equator.

For thirty years, climatologists have been gathering the shards of a broken vase. Each climate model is its own shard, and they all promise different warming by 2100, from 1.5 to nearly 6 degrees. The spread does not shrink no matter how much the models are improved.

Three bodies attracting each other by universal gravitation: a problem that has stumped mathematics for three centuries. After Poincaré, it became clear that no general solution exists and trajectories are chaotic. But within this chaos there are islands of order: periodic orbits where motion repeats.

A fractal that looks like a butterfly hides an order that is not visible at first glance. In the quantum world of one-dimensional quasicrystals described by the Komoto model, the energy spectrum forms a whimsical shape: the Komoto butterfly.

Physicists have created a quantum analogue of a musical instrument. Its “notes”—the allowed energy levels — precisely replicate the first numbers from a set that governs the distribution of primes. These numbers are the imaginary parts of the zeros of the famous Riemann zeta function, a mathematical object inextricably linked to prime numbers.

Drop honey onto a sponge. It lazily creeps, avoiding the voids. But if the honey becomes thinner under pressure, the flow gets trickier. Liquid with variable thickness in an uneven labyrinth of pores — a problem that had defied calculation. The authors of the new work averaged the chaos of microchannels into simple equations.

Graphs are considered identical if their 'terrain' matches. Imagine two maps with mountains and valleys: even if drawn differently, the heights and steepness of slopes can be the same.

Water in a glass settles down once you stop stirring it. Oil in an engine dampens vibrations. It seems viscosity is always about damping. But in some flows, it's the opposite: add friction, and waves start to grow as if from nowhere. Physicists have found a simple explanation.

The diffusion equation, a mathematical tool describing how particles spread out in space, has long painted a paradoxical picture: a disturbance, like ripples on Water, instantly engulfs the entire universe. This challenged the theory of relativity, which holds that nothing can move faster than light.

A regular wall clock runs smoothly, but quantum clocks are a different story. They tick at random moments, and each tick can have a different duration. On average, if you watch such a clock for a long time, it will show the correct time. But at any given moment, its hand might jump forward by an unexpected amount.

A drop falls into a glass, and a tiny jet, a thin fountain, shoots up from the surface for an instant. Something similar happens with a bubble stuck to the wall of a tube when you yank the tube downward. Water around the bubble rushes in, and a jet fires from its top. The speed of this jet depends on the bubble's shape — how much it bulges, like an umbrella dome.

A superconductor is a material that, at very low temperatures, conducts electricity without losses: electrons move without bumping into each other, like a crowd walking down a perfectly smooth corridor. But turn on a strong magnetic field, and vortices appear inside the superconductor — tiny regions where superconductivity vanishes.

A charged particle spiraling in a magnetic field doesn't stay silent: it emits light. This light is called synchrotron radiation, and it shows up everywhere — from distant galaxies to laboratory accelerators.

Two people read the same book, but one turns the page first and then looks at the text, while the other does the opposite. It would seem the result is the same. But in the quantum world, the order of operations changes everything. This work examines models that output sequences of symbols, like a ticket machine.

Quantum entanglement works like a leash: it ties particles together, but the length of this tether is strictly limited. In a chain of particles, heat plays the role of an impatient dog tugging at the leash — the hotter it gets, the shorter the distance over which the connection holds.

A coin toss seems random, but in reality, physics decides everything: the force of the throw, air resistance, the surface's elasticity. If you knew all the details, you could predict the outcome. True randomness lives deeper — in the quantum world.

A branching network, like a river delta or a tree crown, is built on the principle of economy. The classic law, derived back in 1926, stated that the cube of the parent vessel's diameter equals the sum of the cubes of the daughter diameters. This rule worked beautifully for ideal tubes, but real arteries stubbornly gave a different exponent — around 2.7 instead of 3. The authors of the new study found the reason.

A sheet of graphene one atom thick is like a perfectly smooth tablecloth on which electron marbles roll. Place an electric barrier in their path, and usually they'll bounce back. But in graphene, it's different: under certain conditions, electrons pass through the barrier without even noticing it, as if the wall were made of mist.

Black holes are famous for their dark silhouette against a bright glow. It's not actually a shadow, but severely bent light curving around the object. Yet the cosmos also hosts impostors — ultra-dense bodies without an event horizon that warp light in their own distinct way. These distortions can reveal the ruse.

The quantum world loves order, but reality often brings disorder. In this work, physicists study one-dimensional chains of spins — tiny magnetic arrows that can point up or down. Usually, topological phases (stable states protected by symmetry) are defined for pure states, where each arrow is precisely known.

An electron in an ordinary wire is like a courier carrying both a package and the recipient's signature at once: its charge and spin are always together. But if the wire is made just one atom thick, the courier gets cramped. In such a one-dimensional tube, electrons cannot overtake each other, and their collective behavior changes beyond recognition.

Water can be ice, liquid, or steam. Physicists call these states phases. In theory, each phase has its own measure — a way to describe how likely it is. But not every measure you can imagine occurs in nature. Some phases are real, while others are just mathematical illusions. Scientists have found a simple criterion that separates reality from mirage.

A wet sponge sits in a bucket of water. Something massive drifts by, and the sponge stretches slightly toward it because the water pressure is uneven. A neutron star behaves similarly when another star passes nearby: tidal forces stretch it, and it subtly changes shape.

A stone drops into a pond — ripples spread out and vanish. But in a narrow channel, a wave sometimes gathers into a hump and rolls on, unchanging in shape, kilometer after kilometer. Such stubborn solitary waves are called solitons. And if the crest is not smooth but pointed, like a spring compressed to its limit: that's a peakon.

In a big city after rain, water collects in the same low spots no matter where the first drops fall. An hour later, the pattern of puddles hardly depends on where the downpour started. That is equilibrium — the outcome a system reaches regardless of its start, once the details are forgotten.

When two black holes merge, a new black hole is born. At first, it quivers like a struck bell, and this quivering spreads through space as waves. Detectors on Earth catch these waves — from them, we can learn the mass and spin of the black hole. But the signal is weak and full of noise. If you take different chunks of the recording, they might give slightly different answers.

A balloon inflates on its own, even though no one is blowing it up. That's roughly how the accelerated expansion of the universe looks, and to explain it, scientists usually invoke dark energy, an invisible and poorly understood force. But what if the balloon expands because new air molecules are continuously appearing inside it?

Strike a bell, and it responds with its own note. Likewise, a black hole disturbed by the fall of a star or another black hole begins to 'ring,' emitting gravitational waves. But instead of sound, it's the trembling of space itself, and instead of a single note, a whole set of decaying frequencies. These are called quasinormal modes.

In particle physics, it has long been taken for granted that the forces of nature (electromagnetism, the weak and strong interactions) obey a strict symmetry called gauge symmetry. It's like a set of rules by which particles exchange force carriers. But where do the rules themselves come from?

A tightrope walker steps along a taut wire. Each step is a search for balance, an instant calculation of forces. In much the same way, Einstein's equations describe how matter and energy cause spacetime to curve.

A black hole is like a whirlpool in a river: anything that falls in can never escape. But it also has an outer zone, the ergosphere, where space itself moves faster than light and drags any object along. Usually, the size of this zone is tightly linked to the hole's mass and spin rate.

A pot of water on the stove eventually settles down: the temperature evens out, the liquid stops boiling. Physicists call this thermal equilibrium — a state where energy is distributed in the most probable way.

Spread a handful of coins on the table. Each coin is a possible outcome: heads, tails, or something else. If we know how chaotic this set is (its entropy), which combinations of probabilities will we encounter more often? It turns out the answer depends on how much chaos we allow.

Throw a stone into a pond, and ripples spread across the water. Throw two stones nearby, and the ripples intersect, creating a pattern of reinforced and canceled waves. That's interference.

A quantum bit (qubit) is a delicate thing. Even a little heat destroys it, like a random nudge topples a crystal wine glass. To protect this fragile information, physicists have built a three-dimensional quantum structure resembling a Russian doll.

An infinite chain of atoms spaced at equal intervals. Shift the entire chain by one step, and the picture doesn't change. That's translational symmetry: the world looks the same wherever you look. You'd think such a simple rule would give rise to simple states, like a crystal lattice assembled from identical building blocks. But the authors counted those blocks anew.

A drop of honey spreads slowly across a table, while water spreads quickly. The resistance to flow, viscosity, differs from one fluid to another. But what if the viscosity changes on the fly, as the substance compresses or expands?

The quantum world is usually drawn with points, but real instruments only see blurry spots. Heisenberg and von Neumann long suspected: precision is unattainable.

Spacetime isn't a flat sheet, but a crumpled fabric: stars and planets leave creases on it. Information is written into every crease, and to erase it, heat would have to be released — that's how Landauer's principle works. Thus, the 'crumpledness' of space can be measured through entropy — the universal measure of disorder.

Gravitational waves are not vibrations of matter, but tremors of spacetime itself, predicted by Albert Einstein. They travel at the speed of light and pass through objects, stretching and squeezing them.