Scientists solve decades-old 2D physics puzzle — Chaotic growth in a 2D quantum system obeys statistical laws

When you buy through links on our articles, Future and its syndication partners may earn a commission.

Researchers at the University of Würzburg have demonstrated, for the first time, that chaotic growth in a 2D quantum system follows the Kardar–Parisi–Zhang (KPZ) equation , confirming a 40-year-old physics theory. For decades, physicists have believed that even highly disordered growth — from spreading flames to growing bacteria — follows hidden statistical rules.

Until now, the KPZ model, which describes how rough, uneven surfaces evolve under random conditions, had only been verified in simple, single-dimension systems, as extending it to more realistic 2D environments remained experimentally out of reach due to the extreme speeds and scales involved. The researchers’ findings , published in the Science journal, close a long-standing gap in the field, proving that the theory does indeed extend to 2D systems

This breakthrough improves scientists' understanding and modeling of complex growth processes in real-world, non-equilibrium systems.

“When surfaces grow — whether crystals, bacteria, or flame fronts — the process is always nonlinear and random. In physics, we describe such systems as being out of equilibrium,” explained Siddhartha Dam, a postdoctoral member of the research team and co-author of the paper.

“Engineering a system capable of simultaneously measuring how a non-equilibrium process evolves in space and time is extremely challenging — especially because these processes unfold on ultrashort timescales. That’s why verifying the KPZ model in two dimensions has taken so long. We have now succeeded in controlling a non-equilibrium quantum system in the laboratory — something that has only recently become technically feasible,” he continued.

To achieve this, the team engineered a highly controlled quantum system using a gallium arsenide (GaAs) semiconductor cooled to −269.15°C (−452.47°F), near absolute zero. By continuously illuminating the material with a laser, they generated short-lived hybrid particles known as polaritons — a mix of light and matter that form and decay within picoseconds.

These polaritons behave like a rapidly evolving “growth” system. As they are created and spread across the material, their distribution changes in both space and time, allowing researchers to track how the system develops under inherently random conditions.

Using spectroscopy and Michelson interferometry, the team was able to precisely monitor this evolution, capturing how fluctuations in the system scale and spread. Their analysis revealed that the behavior of the polaritons closely matches the statistical patterns predicted by the KPZ equation in two dimensions.