knots

In a mountain range, there are trails that can be contracted to a point if you walk through a flat valley. But there are also loop routes that cannot be shrunk without crossing a ridge.

In a mountain range, there are trails that can be contracted to a point if you walk through a flat valley. But there are also loop routes that cannot be shrunk without crossing a ridge.

Collagen is the rope from which our tendons, skin, and bones are woven. Each "rope" is a bundle of molecules twisted into a triple helix, like three strands in a cable. Until now, no one had seen what happens to these strands when we pull on the cable.

A handful of coins drops onto a table — heads and tails land wherever they please. The same goes for an instantaneous snapshot of a quantum chain: in some places a particle is present, in others it is not. But behind the disorder lurks a precise angle. In this work, a chain of particles closed into a ring was considered. It was divided into four arcs: two were measured, two were left untouched.

A laser beam is like a swift vortex that briefly captures a passing electron. As the particle moves through the pulse, its spin (the intrinsic rotation, like a tiny top) experiences a weak kick. After leaving the beam, the top no longer points in the same direction; it has turned a little.

A quantum chain is like a string of lights, where the bulbs are the spins of particles. Ideally, all bulbs glow in sync, following a common rhythm: that's symmetry. But if you cut off a piece of the string, the rhythm can get out of step: within that segment, symmetry is broken. Physicists study a chain of strongly interacting particles (the XYZ model).

A carousel doesn't just spin you around in a circle — with each revolution, it also slightly screws itself into the ground. This corkscrew-like motion is the essence of the NUT charge, a special property of spacetime that physicists have been studying since the mid-20th century.

Two threads hang in space. One is looped around the other — physicists call this braiding. For a long time, it was thought that the rules of this dance were rigidly set by the number of dimensions. But the authors of the work found a new maneuver: a special kind of braiding that works in one dimension less than usual.

Dim the lights. The stage belongs to a shadow theater, with just r puppeteers, but the screen obeys the laws of hyperbolic geometry. Every wave of the hand births a pattern that mathematicians call a discrete group of isometries.

A sheet of rubber is squeezed from two sides. At first glance, it's just deformation. But inside, deep within the material, a hidden order awakens. This is not just wrinkles on the surface. It's the birth of special zones where vibrations become trapped, as if in a cage. Previously, it was thought that such effects require intricate lattices and periodic structures.

Many cutting-edge physics calculations hit a brick wall — not for lack of ideas, but because of arithmetic. We're talking about integrals that express particle collision probabilities or the shape of gravitational wave bursts.

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.

Light from an ordinary bulb seems utterly chaotic: its waves oscillate out of sync, like a crowd where everyone walks in their own direction. Such light is called incoherent. For a long time, it was believed that elegant topological structures (knots, rings, links) could only be created in coherent laser light, where all waves march in step.

Take a long thread, close it into a ring, and tie a knot in it. The knot slides along the thread until it hits something. Now imagine the thread is made of two different segments: one stiff and slippery, the other soft and sticky. When heated, the sticky segment softens, and the knot can slide off it, like a sled sliding off a melting hill.

In the first moments of the universe's existence, space was filled with hot plasma, where particles emerged and disappeared like bubbles in a boiling pot. The traces of these processes, stretched to gigantic sizes by expansion, are preserved in the cosmic microwave background — ancient light that has reached us across billions of years.

A cell about to divide first marks its waist. Beneath its membrane, in a thin gel of protein filaments, movement begins. The filaments flow like a slow river, and a belt forms in the middle of the cell. This belt tightens more and more until the cell is pinched in half. Scientists built a computer model of this process.

A flexible thread, coiled into a loop, was locked in a tiny box with liquid. It can either absorb water and swell like a sponge, or expel the moisture and shrink into a tight ball. The choice between these states depends on whether the thread has a knot – and which one. The reason lies in entropy, a measure of disorder.

A drop of water with tiny particles dries on a table. The water evaporates, leaving the particles behind, and they arrange into a pattern, like sand after the tide. But if the particles are soft, the pattern turns out quite different. Researchers studied this process under a microscope, varying only one property of the particles: their elasticity.

An ordinary rubber strip filled with fine iron filings doesn't just bend in a magnetic field: it ties itself into a stable knot. This effect was predicted and reproduced in experiments by physicists working with magnetoactive elastomers: a silicone base with carbonyl iron particles.

Inside a piece of magnetic material, electron spins, tiny magnetic arrows, usually arrange into simple patterns. Sometimes they swirl into vortices, like water down a drain, and these vortices can tie themselves into knots.

Snap the bottom of a soda can: it will dent inward and stay that way. Press again: it pops outward. That's bistability: a system with two stable states, like a light switch. An elastic arch is the simplest example. It can curve upward or downward, and to flip it, you need to apply force.

Two particles cling to each other like climbers on the same rope and fly toward a wall. When they hit, will they bounce off together, or will the rope snap? What does it depend on? Physicists considered the simplest case: everything happens on a single line, the particles attract only when they occupy the same point, and the wall is perfectly rigid.

A handful of magnetic beads, when shaken, clump together. But add springs that push the beads apart at a distance, and the clumps break up into neat islands. Roughly this is how the particles in the new study behave: they attract at close range but repel from afar. The authors simulated millions of variants of this 'glue with springs' on a computer.

Open systems exchange energy with their surroundings, like a guitar string fading into the air. Scientists built such a system out of light, twisting the beams into corkscrews and forming an artificial lattice — a maze where losses can be controlled at every step. Light in this maze always moves at the maximum possible speed, but its energy can fade or grow.

All matter, from stars to humans, is built from particles that in the Standard Model are divided into two families. But there's a third, rare kind — particles that, when swapped, don't just exchange places but tie themselves into a knot, remembering the intertwining rather than the path.

Light consists of portions — photons. Max Planck was the first to understand that light is emitted in quanta. Today, we can guide single photons. When such a photon encounters a fast shutter, it cannot be sliced — half a photon doesn't exist. Instead, a quantum mixture of states with different photon numbers emerges: zero, one, two, three..

In a chain of cold spins stretched along a single line, order and disorder can intertwine into a pattern that defies the usual rules. Two states of matter, two kinds of "order," are separated by a crossroads where the roads do not converge but diverge.

In 1979, Su, Schrieffer, and Heeger proposed a model that explained the strange electrical properties of polyacetylene, an organic polymer that conducts electricity almost like a metal. Their chain consisted of carbon atoms connected alternately by single and double bonds.

A stone falls into water, and ripples spread outward. In the quantum world, a magnetic impurity (that pebble) in a metal perturbs the surrounding electrons, and they form a special cloud around it. This is called the Kondo cloud. Like ripples on water in the dark, it long remained elusive.

A crowd in a square. At first, everyone spins to their own rhythm, but suddenly the music changes, and they all start moving in sync, as one. That's roughly how electrons behave in some metals: they either cling to magnetic impurities or break away and form a collective order.