Scientists Finally Solve 40-Year-Old Physics Puzzle About Universal Growth
Researchers achieve first experimental proof that the Kardar-Parisi-Zhang theory holds in two dimensions using quantum light-matter particles.
In a major breakthrough that resolves a decades-old physics mystery, scientists at the University of Würzburg have experimentally confirmed a universal growth law in two dimensions using a quantum system of fleeting light-matter particles. The achievement strengthens the idea that wildly different processes—from crystals forming to living systems expanding—may all follow the same hidden mathematical rules, regardless of their apparent differences.
Understanding how surfaces grow has long been one of physics' most important challenges. In 1986, researchers introduced the Kardar-Parisi-Zhang (KPZ) equation, a theory designed to describe growth across a wide range of systems. Over time, this framework has been applied to everything from crystal formation and population dynamics to flame fronts and even machine learning. The central idea is both simple and powerful: very different systems may follow the same underlying rules when they grow.
"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," explains Siddhartha Dam, a postdoctoral researcher in the Würzburg-Dresden Cluster of Excellence. "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."
To test the theory, the researchers designed a highly controlled quantum setup using a semiconductor made from gallium arsenide cooled to −269.15°C and continuously stimulated with a laser. Under these extreme conditions, unusual particles called polaritons formed inside the material. Polaritons are hybrids of light and matter, combining photons with excitons, and they exist only briefly under non-equilibrium conditions. Created by the laser, they disappear again within a few picoseconds, making them ideal for studying rapid growth processes.
"We can precisely track where the polaritons are in the material. When we pump the system with light, polaritons are created -- they grow. Using advanced experimental techniques, we were able to quantify both the spatial and temporal evolution of this growing quantum system and found that it follows the KPZ model," Dam explains. The successful confirmation in two dimensions, following earlier one-dimensional verification in 2022, represents a significant milestone in demonstrating the truly universal nature of these growth patterns across vastly different physical systems.
