quantum chaos

The quantum world is often compared to a musical instrument. Each system, whether an atom or a chain of particles, sounds at its own frequencies, which physicists call energy levels. In chaotic systems, like an orchestra without a conductor, these frequencies usually fill the entire available range without gaps.

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

Musicians in an orchestra each play their own part, not hearing the others. In a perfect crystal of tungsten disulfide on graphene, excitons, bound electron-hole pairs, behave the same way: they barely mix due to a hidden symmetry called the valley. The energy levels of such a system resemble notes sorted into separate folders — the chaos is incomplete.

A string sounds perfectly pure until a draft touches it. That's roughly how a superradiant laser works: a beam of atoms, pre-charged with energy, flies through a room made of two mirrors — an optical resonator (a trap where light bounces back and forth).

A light beam approaches a black hole not head-on, but at a glancing angle. If the angle is just right, the light neither falls in nor escapes: it starts looping around, like a figure skater circling the rim of a funnel. This narrow track is the photon ring. It acts like a lens, repeatedly reflecting the image of everything that falls into the hole.

Every isolated quantum system inevitably moves toward thermal equilibrium — a state where all details of the past are erased. It’s like an orchestra: instead of a symphony, it starts playing white noise — random but statistically predictable notes.

When hot soup cools, clumps form on the surface — similarly, as the early universe cooled, it gave birth to threadlike clumps of energy: cosmic strings. Some of them are like a stretched rubber band: as long as it's intact, it's stable. But if you nick the band, it snaps.

Gravitational wave detectors work like sensitive microphones, picking up the trembling of space from distant cosmic catastrophes. When two black holes merge into one, the newborn object rings like a bell, and that ringing is a unique 'voice' of gravity.

A figure skater glides across the ice, gradually approaching the center of the rink. A slight twist of the torso, and the smooth spiral breaks, the trajectory becomes unpredictable. Something similar happens when a small black hole with its own rotation (spin) falls toward a giant black hole.

A chemical reaction resembles passing through a turnstile: a crowd creates chaos and gets stuck, while an orderly line moves. In the quantum world, however, when the jostling subsides, the barrier can become ghostly — a particle passes through it as if the turnstile has vanished.

In a pot of boiling water, steam bubbles rise and pop. In the quantum world of a superfluid, bubbles behave differently: they can collide and give birth to vortices — tiny swirling flows, like whirlpools in a river. Scientists modeled such a liquid using a holographic approach.

A thin stream of water on a shower glass gathers into winding rivulets that quiver and shift before your eyes. Such a liquid film flowing down a vertical surface is a classic example of chaos in nature: it all flows downward, sure, but the surface lives its own unpredictable life.

The quantum world is full of surprises: even simply observing a particle changes its behavior. In a new study, physicists showed that continuously measuring energy can make quantum chaos more pronounced. They used a quantity that indicates how long a quantum state remains similar to itself under repeated measurements.

In 2019, the Event Horizon Telescope gave humanity the first image of a black hole's shadow. Since then, astrophysicists have dreamed of more: seeing how matter moves in the very funnel of spacetime. One of the mysteries is chaos.

Five superconducting qubits on a chip: the stage for a performance of quantum chaos. Four qubits form the system, and the fifth acts as the environment, introducing dissipation. After a short evolution, the environment is discarded, leaving the system with an open quantum map, an operator that transforms the system's state.

Imagine a translator who learns the grammar of a chaotic language from textbook examples and then becomes fluent in real speech, complete with accents and noise. That is how the new KDL method works: first, a neural network is trained on synthetic data generated by the Liénard equation, then it is transferred to real time series where extreme events are rare and unpredictable.