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

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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.

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