exponential growth

On a steep mountain slope, a single falling rock sometimes triggers an avalanche, and sometimes gets stuck. It all depends on the state of the slope.

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.

In 1970, mathematician John Conway invented the Game of Life — a cellular field where just three rules generate surprisingly complex patterns. Forty years later, SmoothLife appeared: a version where space is no longer cellular but smooth, like a blurred patch. The authors of the new study took an even simpler variant of this continuous game: now everything changes smoothly in time as well.

A quantum computer relies on two forces: entanglement (particles behaving as a single whole) and "magic"—a measure of how far a state is from familiar classical physics. But how these two resources relate as a many-particle system evolves in time has remained a puzzle. The authors approached the problem through time.

Forget the flat sheet: embryonic tissue is a dynamic landscape of hills and folds. On convexities, cells stretch; in concavities, they compress, as if performing a dance governed by laws eerily similar to spacetime curvature.

The frost pattern on a windowpane doesn't spread uniformly: it sprouts branches, captures new areas, sometimes sealing off voids. This growth is not a smooth expansion but a series of leaps. This image resonates surprisingly with a mathematical model devised by Charles Loewner a century ago.

In the first moments after the Big Bang, the Universe was not a silent void but a seething cauldron of plasma, threaded with sound waves. As the temperature dropped, the cosmos underwent phase transitions — spontaneous reorganizations that gave birth to bubbles of a new phase.

A living organism is a machine that constantly channels energy through itself and converts it into heat. This internal cycle is called internal entropy production (a measure of energy dissipation). But about 2.5 million years ago, our ancestors switched on a second loop — an external one. They picked up a sharpened stone, and then a burning branch.

Inflation is the ultra-fast expansion of the universe in its first moments. It was driven by a field resembling a ball rolling down a hill. But there could have been a second, almost imperceptible ball nearby. The authors of this work considered exactly that scenario: a light spectator field (the axion), frozen at the top of its potential.

Imagine a library where instead of books, you have every conceivable combination of a few dozen quantum particles. The number of combinations grows like a snowball: add one particle, and the volume doubles. For fifty particles, there are more shelves than atoms in the visible universe.

Cosmology has long sought a loophole behind the Big Bang. Inflation, proposed by Alan Guth, stretches and smooths out primordial inhomogeneities, but what lit the fuse itself?

Toss a dozen coins on a table. The number of heads-and-tails combinations is just over a thousand. For two dozen coins, it's already a million. The number grows as 2 to the power of the number of coins, and that's fast. But quantum systems are far richer. Each particle here is not a coin with two sides but an arrow that can point in any direction.

The Universe is like an inflating balloon. Quantum mechanics forbids measuring exactly how big it is and how fast it's inflating at the same time. This principle permeates the cosmos: a new equation states that the Universe's expansion and its size are linked by a fundamental uncertainty.

Drop a stone into a pond — ripples spread across the water. The most visible ripple comes from the strongest splash. That's roughly how physicists picture the growth of perturbations around a black hole: if a system has an instability, its 'loudest' component, the one that grows fastest, should show up first.

Tiny magnets on a lattice, the classic Ising model, are usually described by how neighbors influence each other. But what happens when the system is closely watched? Each measurement of a coupling energy is like a gaze that forces the magnets to 'decide' their state.

To understand how the universe emerged from the Big Bang, physicists look to Georges Lemaître's idea of expansion, which rests on the laws of Hendrik Lorentz. One daring approach replaces elementary particles with giant tables of numbers — as if instead of the usual roulette balls, you use numbered cards.

A fisherman casts a net into a quiet backwater. The longer the rope, the weaker he feels the faintest nibble — the wave fades along the way. But what if the signal didn't die out but grew stronger? That's roughly the trick described by the authors of a study on an ensemble of particles placed in a field with a special 'stepped' force gradient.

Imagine inflating a balloon. At first, it expands slowly; then someone gives a sharp blast of air, and it swells faster. But as the airflow weakens, the balloon's growth slows again. According to a new study, the Universe has behaved much the same way: after the Big Bang, it expanded, then suddenly accelerated, and now that acceleration is fading.

Before measurement, a quantum object lives in a world of possibilities, where wave amplitudes add up like sound waves in a studio before pressing the “record” button. Crests amplify each other, troughs cancel out.

In the quantum world, the path to calm sometimes resembles a paradoxical race: starting further from the finish, the system reaches equilibrium faster. This effect, a quantum analog of the Mpemba phenomenon, is due to the rapid growth of entropy — a measure of disorder.

For a long time, cosmologists could not peer beyond the starting point — the infinitely dense singularity of the Big Bang, where the equations of general relativity by Einstein lose their predictive power.

Finding the largest group of strangers among a crowd is a challenge that pops up in logistics, chemistry, and scheduling. Ordinary computers hit a black hole here: not from lack of power, but because the problem's structure swallows any classical solution. The new quantum algorithm sidesteps the trap.

In 1961, Stanislaw Ulam proposed a simple model: a particle bounces between a fixed wall and a wall that oscillates according to a piecewise-linear law. It seemed like just another billiard. But behind this simplicity lay a question that troubled physicists for decades: can the particle accelerate to infinity? The answer turned out to be paradoxical. In the classical version, almost never.