Coulomb's law

Two dancers on the same stage mirror each other's moves even when a curtain separates them. In the quantum world, such pairs are called entangled, and physicists have spent half a century probing how far this connection reaches. Until now, all tests with massive particles concerned their internal properties, such as spin, but not their motion itself.

Two electrons that leave a metal needle tip almost simultaneously start to repel each other, like two people trying to squeeze through a narrow door at the same time. The closer they are, the more they get in each other's way.

On the wall: light and dark fringes. That’s what light looks like when it cancels itself out. Way back in the 17th century, Christiaan Huygens suggested that light is a wave.

Imagine a quantum phase transition as an intricate dance. Electrons whirl in strict order, each step representing their spatial arrangement, and the rhythm their dynamics. For decades, physicists could only see a blur of motion, unable to tell if the figures were changing or the music speeding up.

DFTB is a high-speed train in the world of quantum chemistry: hundreds of times faster than classical DFT, yet still on electronic rails. But its engine — iterative self-consistency of charges — sometimes resembles an orchestra where each instrument starts from an arbitrary note.

The quantum many-body world is a jazz ensemble, where each electron improvises, continuously listening to all the others, and the overall wave function is born from this tense dialogue.

The early universe expanded at a breakneck pace: this phase is called inflation. But how exactly did it do it? Some models describe the expansion as a steep exponential surge, others as a more gentle power-law motion.

Fast radio bursts (FRB) — mysterious beacons of the Universe, emitting in milliseconds energy comparable to the Sun’s radiation over centuries.

For nearly forty years, high-temperature superconductivity in cuprates has remained one of the deepest riddles of condensed matter physics.

In the conventional Heisenberg picture, spins at low temperatures are supposed to line up in a strict pattern. But there are crystals — like pyrochlore — where geometry has its own way. Each ion sits at a vertex of a tetrahedron, and the main interaction enforces a rule: two spins point inward, two outward.

Electric charge is not like a number chiseled in stone. In the vacuum around any charged particle, pairs of particles and antiparticles are constantly born and annihilated, like the foam in a glass of champagne. The bubbles screen the true charge, making it appear smaller or larger depending on how close we get.

Inside a crystal, an invisible ballet unfolds: the magnetic moments of atoms, like dancers, sometimes align in unison, sometimes scatter in antiphase. The choreography is dictated by quantum exchange — music sensitive to the geometry of bonds.

The thinner the ferroelectric film, the stronger the depolarizing field — a dictate of classical physics. Imagine a pencil balancing on a fingertip: the shorter it is, the harder to keep it upright. Nanoscale polarization likewise strives to vanish.

Light hits a crystal and knocks an electron out of its rightful place. A void remains — a hole that behaves like a positive charge. The electron and hole attract each other and circle around one another, like a pair in a slow dance. Such a pair is called an exciton (from the word "excitation"). But this dance is not in a vacuum.

The Universe follows strict rules, like players at a table. One of them: gravity always attracts, and energy cannot be negative.

The shape of a riverbed precisely follows the equation describing the growth of a universe with negative curvature. In the lab, water flowing over sand spontaneously carves a cross-section that matches the solution for the Anti-de Sitter model. A river tends toward a shape that maximizes bottom friction.

Two grains of salt fall into a glass of water. They dissolve, and sodium and chloride ions spread throughout the volume. The schoolbook truth is simple: like charges repel, opposite charges attract. But recent experiments with tiny spheres in liquids have revealed a picture that breaks this rule.

Vacuum is not silent emptiness, but a boiling cauldron of quantum fluctuations, born from nothing and vanishing in billionths of a second. This invisible symphony acts like a constant wind, pressing an atom against a wall — as if a powerful bass note pushes a light ball.

To uncover the proton's true size, physicists swapped the electron in a hydrogen atom for its heavy copy — the muon. Acting like a magnifying glass with thousandfold power, the muon gets right up against the nucleus and 'probes' the proton with unprecedented precision.

If you place a kaon in an electric field, it stretches slightly, like a balloon rubbed on wool. This response, the electric polarizability, shows how rigidly the particle is built inside. For the charged kaon, it has been measured for the first time, and the number is about one ten-thousandth of the volume occupied by a proton.

A quantum dot is like a tiny island where one or a few electrons can settle. In this new work, such an island was connected to two 'seas' of electrons: one flat like a pancake, the other bulky like an ocean. Electrons can hop from the island to the seas and back, and this hop depends on the shape of the electron's wave on the island.

A crystal of calcium ions in a trap, illuminated by a laser, is a tiny model of the matter inside a white dwarf. There, in the depths of a dying star, atomic nuclei arrange into a rigid lattice as the temperature drops.

According to ordinary mechanics, an electron in an atom should spiral into the nucleus and crash into it, like a surfer losing speed and falling off the board. But atoms live for billions of years. Because space isn’t empty. Even in absolute vacuum, an invisible electromagnetic sea ripples — the zero-point field. Its waves continuously nudge the electron.

When two different materials are pressed together and then pulled apart, a spark jumps between them. Anyone who has pulled off a wool sweater in the dark or gotten a shock from a doorknob knows the feeling. For a long time, it was thought that charges simply hop from one surface to another due to differences in material properties.

A drop of metal on a semiconductor is like an island in the sea. For an electron to reach that island, it must pay a "toll": overcome a barrier that arises because the island is tiny, and each extra charge significantly changes its energy. This phenomenon is called Coulomb blockade. It underpins single-electron transistors, where current flows one electron at a time.

Since the days of Galileo, it was believed that in a vacuum all bodies fall identically. Einstein elevated this to a principle: gravity travels at the speed of light and is the curvature of spacetime.

The electron is a tiny particle, but inside a crystal it behaves as if it had a different mass. Physicists call this the effective mass. To measure it, they make electrons run in circles in a magnetic field, like a speed skater on an ice rink who is kept from leaving the orbit.

Water in a puddle after rain swirls differently than in a deep lake. A thin layer of fluid feels the bottom, and that changes the nature of its vortices. Scientists created such a layer in the lab: they poured in an electrolyte, ran a current and a magnetic field, and the fluid began to move.

Six barium ions lined up in a flat hexagon inside a Paul trap, a device that holds charged particles with oscillating electric fields. But a slight change in the shape of the trapping potential made the crystal rearrange: one ion moved to the center, and the other five formed a ring around it.

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.