time evolution

In a rubber band stretched in the lab, three different elasticity mechanisms operate simultaneously. At small strains, Hooke's law prevails; at intermediate strains, entropic chain elasticity; at large strains, strain-induced crystallization.

The interpreter in the meeting room hears the shift in tone before it is spoken aloud. They catch subtle changes in breathing, pauses, and intonations, and already know that in a few minutes the conversation will turn heated.

When a fluid flows around an obstacle, it spawns vortices and shock waves. Describing their behavior means solving a nonlinear equation in which the flow velocity depends on itself. Classical supercomputers spend days on this, while quantum computers have barely been used: their native language is linear operations, but fluids are inherently nonlinear.

A quantum particle moves in a circle, passing through several stations. At each station, something happens to it — for example, its properties change slightly. After completing a full circle, the particle returns, but its state is no longer exactly what it was at the start.

The quantum world is like a kitchen where particles suddenly appear out of "nothing." But you need a chef — a classical field acting as an external source. Glauber's theorem, long known in optics, has now been generalized: it shows exactly how the field "cooks up" particles, be they photons or gravitons.

A cluster of glowing dots drifts through the darkness, now compressing into islands, now spreading out in waves. These are not fish or birds: this is a mathematical model of active matter, where each particle spends its own energy on movement, and also is born, dies, and competes with neighbors for space.

In the big world, there's a simple rule: energy density can't be negative, and its flow can't outrun light. In a café, that would look like this: a waiter can't deliver orders faster than he can run. Physicists call this restriction the energy dominance condition. But in the microworld, where quanta rule and spacetime can bend, energy starts acting up.

Clocks in the Universe are tricky things. Usually, in calculations of the birth of the world, a special scalar field plays the role of a clock — something like an invisible fluid filling all of space. It ticks, and physicists watch how the world changes relative to that ticking. But these clocks are man-made, introduced for convenience. The authors of the new work took a different path.

An optical trap holds an atom almost motionless, like a ball on a soft spring. But as soon as acceleration appears, say gravity, the equilibrium shifts. The atom moves within the standing light wave, and this changes the rate at which it exchanges energy with the field. The frequency of this exchange becomes a direct indicator of acceleration.

Cosmic ripples begin with tiny clumps. 380,000 years after the Big Bang, the universe was nearly homogeneous — density fluctuations were only one part in 100,000. But gravity turned these weak ripples into galaxies, clusters, and giant voids.

A stable system behaves like a ball in a bowl: give it a push, and it rolls back to the bottom. The spread of possible trajectories, uncertainty, shrinks over time. But the speed depends on the slope of the bowl's walls. In complex systems, this 'bowl' has sections of varying steepness.

Photographing hummingbird wings with an ordinary camera gives a blurry smudge. For a sharp picture, you take many rapid shots from different angles and piece them together: that's how a quantum 'snapshot' is made. In the lab, scientists 'feel' the vibrations of a tiny mirror with a laser beam.

Crystals fascinate us with their perfect spatial order: atoms frozen at lattice points, like beads on an invisible string. But what if the same symmetry unfolds in time? Time crystals are systems that, without any external cue, start repeating their states cyclically — clocks wound by nature itself. Inside this tireless rhythm, disorder seems to have no place.

A quantum wave is like a long-exposure photograph: everything’s blurred, but the blur itself reveals motion. Usually these frozen waves are treated as convenient abstractions. Yet if at each point in the image you estimate, by brightness, the moment on the particle’s internal clock it landed there, flat space suddenly acquires curves.

In the ocean, a whirlpool pulls everything into a closed loop, just as a gravitational wave in empty space twists time into a loop. Gravitational wave — a ripple in the fabric of spacetime, and its special shape can turn the usual flow of events into a closed cycle. In such a zone, an object can return to its own past without violating the laws of physics.

A sugar cube dropped into tea dissolves, and soon the entire liquid is uniformly sweet. This path to equilibrium is so familiar that it seems obvious.

A regular object moves along a predictable path, like a ball. In the quantum world, a particle is smeared into a probability cloud. To find order in this fog, scientists have recast Schrödinger's equation in the language of flowing water.

The void is never truly empty. In curved spacetime (for instance, in an expanding universe or near a black hole) the vacuum heats up. This is reminiscent of how acceleration makes particles appear seemingly out of nowhere: a phenomenon known as thermal vacuum radiation.

The river of time may not be a smooth flow but a sequence of minuscule steps, like a stop-motion film shot with an unimaginably fast camera. In 1964, Yu. A. Golfand suggested that time moves not continuously but in tiny jumps, and derived an equation that predicted an inevitable increase in disorder (entropy).

You can think of a political system as a vast galaxy — a gravitationally bound system of stars, gas, and dust. In this analogy, parties are the stars, radiating the light of public activity, while their supporters are dark matter, the invisible substance that emits no electromagnetic radiation but whose mass holds the whole structure…

Since the end of the 20th century, we've known: the expansion of the Universe is accelerating — galaxies are flying apart faster and faster. The discovery brought a Nobel Prize to Adam Riess, Saul Perlmutter, and Brian Schmidt.

In the scorching heart of a dying star, an invisible stream is born — a neutrino gas. The particles race through matter almost without stopping, but when their density is enormous, they start to feel each other. Old calculations described this as a jostle in a crowd: each shove changes direction, but no connection arises between passersby.

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.

A thrown stone follows a smooth arc: its path is easy to predict. But if the stone skips across water, the trajectory becomes jagged and far more interesting. Quantum particles behave much the same way when their state is not a calm wave with fixed energy but a turbulent mix of several waves at once.

Time in physics is like a conductor setting the tempo for the whole orchestra. But in the quantum world, there's no single baton: each particle can live by its own clock. Usually, we simplify the picture and assume time flows the same for everyone.

A quantum cat is a special state of light, the idea of which was proposed by Erwin Schrödinger in his famous thought experiment.

For almost a century, cosmologists have been grappling with the mystery: what makes the Universe expand ever faster? The standard answer — dark energy — creates a monstrous discrepancy between the theoretical vacuum density and observations. But there's another path, one that turns causality on its head.

A candle flame in a draft dances: now it flares up, now it almost goes out. Quasars behave much the same way — supermassive black holes in the centers of distant galaxies, surrounded by a scorching disk of infalling matter. Only they flicker not over seconds, but over months and years.

A taut sheet wrinkles. If you tug a corner, a smooth wave runs across; if you sharply bunch the fabric, a sharp crease forms. Space and time in Einstein's equations behave much the same way. Gravitational waves resemble the gentle ripples of the sheet, while shock fronts are like stiff folds where matter's properties change abruptly.

An eternal Universe where the measure of disorder (энтропия) grows is, for most of its time, a homogeneous void. In it, complex structures occasionally assemble by chance, such as fleeting consciousnesses — ‘мозги Больцмана’.

If you accelerate one of four entangled particles to enormous speed, their quantum entanglement doesn't just melt away: it first weakens, then strengthens again. Physicists discovered this unexpected twist while studying the behavior of a special state called the Dicke state in a world governed by the laws of relativity.

The deepest equations of physics, like the Wheeler–DeWitt equation, contain no time. Past and future are scrambled within them, like frames on a film reel with no arrow indicating which way to play it. This symmetry is not a flaw but a feature.

The universe is not a solid monolith, but a canvas of countless quantum threads. Spacetime doesn't flow like water, but vibrates like a tapestry in the wind. For a long time, physicists only saw the overall pattern, neglecting the tremor of individual threads.

Modern detectors of gravitational waves confirm that black holes are real. Spacetime can be compared to a giant trampoline: massive stars make it sag.

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.

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.

On the surface of a tiny sphere live two invisible fields, like two kinds of ripples on a soap bubble. These fields don't just oscillate on their own: they constantly influence each other, like musicians playing in unison. In a new study, physicists derived exact equations that describe how this ripple changes over time, heats up, and descends into chaos.

A stone falls into a pond, and ripples spread across the water. They reflect off the shore, overlap, and die out. All this motion unfolds in space. But what if the pond itself changed its depth or density for an instant — not at one point, but everywhere at once? A temporal boundary is exactly such a jump in properties over time, not space.

Classical general relativity predicts: a singularity hides inside every black hole. In this region, spacetime curvature skyrockets to infinity, and Einstein's equations lose meaning.

A boiling pot, a gust of wind, a wisp of smoke from a campfire — all obey equations that mathematicians call 'nonlinear and dissipative.' In plain terms, energy is lost to friction, and parts of the flow influence each other so strongly that predicting the motion ahead of time is a task on the edge of feasibility.