Physicists Confirm Universal Growth Law Using Quantum Light-Matter Particles
Scientists achieve first experimental proof of 40-year-old theory in two dimensions, strengthening idea that wildly different processes follow same hidden rules.
Scientists at the University of Würzburg have achieved a major breakthrough in physics by experimentally confirming a universal growth law in two dimensions using an exotic quantum system. The research represents the first experimental proof that the Kardar-Parisi-Zhang equation, a 40-year-old theoretical framework, accurately describes growth processes in two-dimensional systems. The finding strengthens the revolutionary idea that vastly different phenomena—from crystal formation to population dynamics—may all follow the same fundamental rules.
The KPZ equation was introduced in 1986 to describe how surfaces grow across a wide range of systems. Over decades, this framework has been applied to everything from crystal formation and bacterial growth to flame fronts and even machine learning algorithms. The underlying concept is elegantly simple but scientifically profound: very different physical, biological, and chemical systems may follow identical mathematical rules when they grow or expand.
To test the theory, researchers designed a highly controlled quantum experiment using gallium arsenide cooled to minus 269.15 degrees Celsius. They continuously stimulated the semiconductor with laser light, creating unusual hybrid particles called polaritons that combine properties of both light and matter. These polaritons exist only briefly under non-equilibrium conditions, making them ideal for studying rapid growth processes that unfold on ultrashort timescales.
"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 at Würzburg. "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."
The successful confirmation in two dimensions follows earlier experimental verification of KPZ behavior in one-dimensional systems achieved by researchers in Paris in 2022. The Würzburg team's achievement represents a significant step toward understanding whether universal mathematical laws govern growth processes throughout nature. The research could eventually lead to better predictions and control of complex systems ranging from biological tissue development to industrial manufacturing processes.
