Fermi–Dirac statistics

A courtroom interpreter is distracted by every rustle: the creak of a chair, a cough in the back row, the rustle of papers. By the end of the day, they are translating not what the witness said, but what they heard through the noise. Rare translation errors are not the result of a single loud shout, but of the accumulation of many small disturbances.

In the quantum world, particles sometimes behave like acrobats on invisible tightropes. An instanton field is a brief vortex that appears and vanishes in an instant. When a fermion (a particle like an electron) enters such a vortex, its energy does not stay put. Instead, it smoothly slides from one level to another, like a ball rolling down a hill.

A fast radio burst is a short but powerful flash of radio waves from deep space. As it travels to us, the signal passes through clouds of tenuous gas, and the more gas it encounters, the more the signal is smeared across frequencies. Astronomers call this delay the dispersion measure — essentially, it's a "weighing" of all the matter along the line of sight.

Some 123 parsecs from Earth, in the constellation Corona Australis, drifts the neutron star RX J1856.5-3754. Its diameter is about 12 kilometers, smaller than Moscow's Ring Road, but its surface temperature reaches 460 000 kelvin. The star emits a slow, almost inaudible exhalation.

The interiors of neutron stars are a realm of degenerate matter. Here, protons condense into a superconducting condensate, threaded by quantum vortices. Imagine tiny magnetic tops: each carries a quantum of magnetic flux and glides through the electron fluid.

The classical Mpemba paradox — hot water freezes faster than cold — has teased scientists for centuries. Only recently has nonequilibrium statistical mechanics explained it: it’s all about boundary conditions; the system seems to seek an excuse to “hit the wall” and speed up cooling.

Spintronics promises to transmit information not by charge but by spin, ridding microelectronics of its main enemy — Joule heating.

Superconductivity and magnetic field are age-old foes: the field barges in like a whirlwind, tearing apart the delicate pairing of Cooper pairs, destroying order.

A pebble falls into a pond, and ripples spread across the water. In the quantum world, the pond is not made of water but of many identical particles, and the pebble is also a particle, just a foreign one. Such a foreign particle is called a Fermi polaron.

Textbooks divide particles into two camps: bosons love to crowd into the same state, fermions absolutely refuse. But nature allows a third option. Anyons are quasiparticles whose behavior lies somewhere in between. They can 'remember' how they were exchanged and obey a nonstandard exclusion principle.

A boiling kettle with the lid on doesn’t show the bubbling, but the sound and vibration betray the intensity of the water boiling.

When an electric charge moves with acceleration, it emits electromagnetic radiation, i.e., light — a familiar phenomenon in physics. However, researchers have found that when moving along a specially chosen trajectory, the radiation acquires unusual properties.

In the microscopic world, the Pauli exclusion principle holds sway: fermions — particles with half-integer spin, such as electrons — cannot occupy the same quantum state. This fundamental rule of the Standard Model forces electrons in atoms to occupy different orbitals, giving matter its volume and structure.

Sunlight hits a silicon wafer, and a current flows in the circuit. That's the familiar work of a solar cell: light knocks out electrons, and a p–n junction (the boundary between two layers with different conductivities) forces them to move in one direction. But in some crystals, current arises differently — without any junctions, purely from the material's internal structure.

If you squeeze a handful of sand in your fist, it first compacts, but then starts to resist — the grains have nowhere left to go. In the depths of a neutron star, something similar happens, except instead of sand grains, you have elementary particles, and instead of your hand, you have monstrous gravity.

Quantum computers promise to solve problems that regular computers can't. But where is the line? The authors of a new study stumbled upon a surprising case: electrons paired up behave like a well-behaved orchestra. Even if you add a bit of "magic"—a special quantum resource: their behavior remains predictable.

In a carbon atom's nucleus, particles occupy their own 'apartments'—like residents who cannot share the same room. Physicists call this rule the Pauli exclusion principle: two identical inhabitants of a nucleus cannot be in the same state. But what if the rule is sometimes broken?

An ultracold cloud of atoms trapped in laser light can 'breathe': it rhythmically contracts and expands, much like lungs. Physicists have long been able to observe this breathing, but only now have they realized that its amplitude is not just a pretty picture: it is a precise measure of hidden energy jitters inside the cloud.

A tiny magnet, made from just two molecules, was placed on a metal surface, and it behaved like a temperamental conductor. Normally, electrons in a metal move in a coordinated way, like a crowd on an escalator. But when cooled significantly, this order breaks down, and the motion becomes unpredictable.

In a pot of boiling water, bubbles of steam are born and pop, but the water itself remains a liquid. Something similar happens in an ultracold atomic gas: atoms constantly form pairs and then fly apart again, even though superfluidity has not yet set in.

In everyday life, time flows on its own, like a river past its banks. But in quantum gravity, things are different: time does not flow; it emerges from relations between objects, like a pattern in a carpet that is only visible when viewed from a certain spot.

A metal is a sea of electrons that move almost freely, colliding only occasionally. But in some materials, this sea suddenly becomes viscous and unpredictable: electrons stop behaving like independent particles. Physicists call this state 'non-Fermi liquid,' and it remains a puzzle.

Physicists trapped a cloud of lithium atoms between mirrors. Light bounces inside, like in an echo chamber, forcing the atoms to emit synchronously — resulting in superradiance, akin to a choir where voices merge into a single thunder. Like a stadium chanting in unison: each whisper turns into a deafening rhythm. The secret is density.

The law discovered by Wolfgang Pauli forbids identical particles from occupying the same spot. Hence, in cold matter, a Fermi sea is born: particles, like water, fill energy levels from bottom to top. The shape of the sea's surface — including 'islands' of emptiness — dictates the properties of the whole system.

In general relativity, a black hole has long been regarded as a perfect mirror: no matter what fields fall onto it, it does not deform. The tidal Love numbers, which measure how a body deforms under an external tidal field, turned out to be zero for scalar, electromagnetic, and gravitational perturbations.

The galaxy NGC 1560 is a modest island of stars and gas ten million light-years away. Its rotation curve, first measured in 1991, became an icon for those seeking an alternative to dark matter. The plot of rotation speed versus radius shows bends that seem to exactly mirror the bends in the distribution of ordinary matter.

In a tropical forest, the dry season gives way to the rainy season, and with the weather, the rules of life change: some animals go into hibernation, while others come out of hiding. Likewise, in complex systems, from climate to economics, the links between processes are not set in stone. They depend on a hidden "regime" that itself switches from time to time.