Wigner function

An airplane wing, like a skier on a ski jump, remembers its acceleration. Change the angle of attack sharply, and the lift does not immediately reach its new value. It builds up gradually, as if the wing is not yet sure the maneuver is for real. This effect was discovered by engineer Herbert Wagner in 1925.

A quantum detector is like a sensitive pendulum suspended in empty space. If a sharp gravitational wave passes by, you might expect the pendulum to swing. But the calculation shows otherwise: the wave doesn't swing it: it damps any existing oscillations.

In the first instants after the Big Bang, the universe expanded faster than light could cross it. Like an inflating balloon, but instead of rubber, it was space itself. On this balloon, ripples inevitably formed — tiny compressions and rarefactions from which all galaxies and stars later grew.

In the first moments of its life, the universe resembled a boiling cauldron. Matter wasn't spread evenly — clumps and voids were brewing within it, and their violent motion gave rise to a trembling of space itself: gravitational waves.

Empty space is not as empty as it seems. According to quantum theory, the vacuum is filled with particles that constantly pop in and out of existence. In 1976, physicist Bill Unruh showed that if an observer moves with acceleration, this 'quantum soup' turns into a genuinely warm bath for them — the Unruh effect.

A delicate watermark on wet paper, and a fogged-up glass before your eyes. That's roughly what reading quantum states of light looks like: fragile photon patterns get distorted by losses, and detectors catch only a small fraction of the signal.

In an ultrathin sheet of four-layer graphene, electrons can behave like a frozen liquid. When cooled strongly and subjected to an electric field, they stop darting around and line up into a regular pattern — a Wigner crystal. It's similar to how water droplets on a frosty morning turn into ice honeycombs.

Ever since Fritz Zwicky noticed that galaxy clusters were moving too fast, and Vera Rubin measured the rotation of spiral arms, dark matter has remained cosmology's greatest mystery.

A black hole is not a dead object. After a disturbance, such as merging with another hole, it rings like a bell. This ring is not just a sound but a complex set of damped oscillations called quasinormal modes. Their frequency and damping rate depend on the hole itself: its mass, charge, and spin.

In the classical picture of the world, gravity is the smooth bending of space and time. But at the microscopic level, where quantum mechanics rules, these bends should turn into a grainy ripple. The particles of such a ripple are called gravitons. The trouble is that straightforward calculations with gravitons always run into infinities — the theory loses its meaning.

A strange visitor came to light in a fleeting flash. A beam of photons struck a deuterium nucleus (heavy hydrogen), and in the cascade of produced particles, detectors noticed something unusual. At a certain combination of masses and momenta, the signal sharply intensified, as if a new particle had appeared for a brief moment.

Picture a pot of boiling soup, but every grain in it is not just a point but a tiny top spinning around its own axis. That's the world of spin-1 particles. For example, some short-lived mesons born in accelerator collisions.

The early universe expanded at an unimaginable rate — faster than light could cross it. In this boiling cauldron, any region of space resembled an open can of paint: its boundaries continuously captured new 'vapor' from outside, while some of its own contents irrevocably escaped.

The light cone is a blueprint of causality, laser-cut onto the fabric of the universe. In classical physics, it is as sharp as a scalpel: events inside are linked by invisible threads of influence, while outside lies eternal isolation, sealed by the ultimate speed limit.

A quantum computer measures a molecule's energy much like an old tape measure that only has markings every meter. If the actual length of a table is 2.37 meters, the tape shows “two and a bit,” and you can't do better. Physicists call this resolution: the step of the grid, finer than which you cannot go. The authors of the new work turn this flaw into an advantage.

The familiar metronomes placed on a movable platform eventually start to swing in sync. In the quantum world, this trick long eluded scientists. But now physicists have synchronized even the most exotic state — a Fock state, where the number of light particles is precisely defined, like in a counter.

A soap bubble hangs in the air, and its shape already contains everything needed to calculate the internal tension. A similar principle worked in a new study on quantum gravity. Physicists took a closed surface, an analog of such a bubble, and specified a few numbers on it: for example, the electric field strength and the curvature.

Gravity is the curvature of spacetime, not just an attraction, as Einstein showed. On such a curved "dance floor", even the hypothetical carriers of gravity — gravitons — move oddly.

You can feel an unfamiliar object along its length, across its width, or diagonally: each time gaining new information. But what if one way of feeling tells you absolutely nothing about what another would reveal? That's exactly how mutually unbiased bases work in quantum mechanics: measuring in one of them leaves you completely in the dark about the outcome in another.

In physics, there's an old ache. General relativity paints the beginning of the universe as a point — a singularity where equations break down and volume shrinks to zero. Quantum mechanics hints that at the most critical moment, something goes differently than classical physics predicts.

Two thin sheets with honeycomb patterns were stacked and slightly rotated, creating a new pattern — a moiré, like the shimmer of silk. The electrons in the experiment behaved similarly: they arranged themselves into two layers, with one layer rotated exactly 30 degrees relative to the other.

A handful of sand lands on the table. The grains settle in different ways, but if the handful is large, the total volume barely changes. That's roughly how classical gravity works: space appears smooth and definite. But look closely at the individual grains, and you'll find that at the quantum level, volume itself is no longer fixed.

A handful of rice grains falls onto a hot skillet, and they start jumping. Each grain pushes its neighbors, and the whole pile stirs without any external hand. That's active matter: a multitude of particles that draw energy on their own and convert it into motion.

Hundreds of people on a dance floor stand at equal distances from each other — strict order, like in a crystal lattice. Slow music is thermal vibrations, making dancers sway slightly. If the music gets louder and faster, order collapses: everyone mixes. That's how thermal motion destroys ordered states of electrons in solids.

A crowd of people suddenly starts moving as one. In physics, this happens with atomic spins — tiny magnetic arrows. When many spins come together and interact through a shared medium, they form one big magnet, or a macrospin. This macrospin doesn't just point in one direction; it can get stuck in several positions, like an ice cube that refuses to melt even when it's warm.

In a strong magnetic field, electrons trapped in a thin layer sometimes arrange into a regular pattern, like guests at a crowded party who find a spot where no one jostles them. This order is called a crystal, although it is not ice or salt, but the electrons themselves, frozen in place.

It all started with tiny quantum flickers on the primal canvas. Inflation — an avalanche-like expansion proposed by Alan Guth — stretched those brushstrokes to the scale of galaxies.

A laser beam inside a special crystal spontaneously turns into a “Schrödinger’s cat”—a mixture of two states. Erwin Schrödinger dreamed up this paradox for an atom, but now physicists see it happen with an entire stream of photons. Light is like a company of soldiers on a parade ground.

In quantum theory, a particle can run along two paths at once. When measured, we catch it on just one. According to Niels Bohr, all other possibilities vanish instantly — like a branch snapped off a trunk. Yet Hugh Everett insisted: the tree of reality grows all its branches at once, and we only see the one we’re on.

The universe is expanding, and scientists want to know how fast and what it's made of. To do that, they compare data from distant stellar explosions, sound waves in the early universe, and the faint glow left over from the Big Bang. Each dataset is like a piece of a mosaic, and the goal is to assemble them into a full picture.

A hundred fireflies in a jar blink out of sync, but once they synchronize, their flashes merge into a bright pulse. Quantum emitters, individual atoms or artificial particles that can emit photons, behave in much the same way. When there are many of them and they interact, calculating their collective behavior is no easy task.

Light trapped in a tiny cavity is like a pendulum that gets pushed harder and harder. At first, it swings smoothly and predictably, like an ordinary clock. But if you push it hard enough, the motion becomes strange: the pendulum seems to be in two extreme positions at once.

Stars on the outskirts of galaxies rotate faster than predicted by the laws of physics if only visible matter is considered. This paradox was uncovered in the 20th century by Vera Rubin and Fritz Zwicky.

A material just one atom thick and of record purity — only one foreign atom per million — becomes the setting for a remarkable phenomenon. When cooled to near absolute zero, the electrons inside, like musicians in an orchestra, freeze into a strict order, forming a crystal. This state, predicted by Eugene Wigner nearly a century ago, has now been observed in detail.

Schrödinger's cat usually hides in thought experiments — alive and dead at the same time. This time, it was caught in the lab: a light pulse was made to be in two opposite states at once, like a coin hovering in the air, heads and tails at the same time.

Electrons in a conductor usually behave like a gas: they dart around chaotically, collide, and don't hold formation. But if you spread them far apart and cool them down, their mutual repulsion can force them into place, like attendees in an overcrowded hall who settle into every other seat.

Two electrons in a narrow tube don't want to be close. Both carry a negative charge and push each other apart, like two magnets with like poles facing. If the tube is very thin, they can't move sideways, so they line up one behind the other. Physicists call this Wigner localization: the particles take fixed positions, like beads on a taut string.

Usually, to understand a quantum state of light, you need to perform dozens of complex measurements, like trying all the keys on a keychain. The new AI model works differently: it's a universal key that, after a slight adjustment, opens many 'locks'—simple and the most tricky states.

Dark matter makes up 85% of the matter in the Universe, yet remains invisible. It only reveals itself through gravity. We can catch it by its cosmic 'hum' — a faint vibration that permeates space. A single detector is powerless here: the signal is too quiet. Physicists turn many sensors into a quantum ensemble.

The Wigner function is a kind of topographic map of probabilities: hills correspond to regions where a particle is most likely to be found, and valleys to where its appearance is practically ruled out.