A 40 year old physics puzzle about how things grow has finally been cracked. Scientists in Germany have experimentally confirmed a universal growth law in two dimensions for the first time. The finding suggests that wildly different processes from crystal formation to bacterial colonies may all follow the same hidden rules.
A theory born in 1986 finally gets its proof
In 1986 researchers introduced the Kardar-Parisi-Zhang equation, a theory meant to describe growth across many systems. The idea was simple: very different systems might follow the same underlying rules when they grow. The theory had been confirmed in one dimension in 2022. But proving it in two dimensions remained elusive until now.
How they built an ultracold quantum experiment
Researchers at the University of Würzburg designed a highly controlled quantum setup to test the theory. They cooled a semiconductor made from gallium arsenide to minus 269.15 degrees Celsius and continuously stimulated it with a laser. Under these conditions unusual particles called polaritons formed inside the material. Polaritons are hybrids of light and matter that combine photons with excitons. They exist only briefly and only under non equilibrium conditions.
The team measured how these particles moved in space and time. This was the first ever experimental demonstration of KPZ universality in a two dimensional system in both space and time. The challenge had been that growth processes are always nonlinear and random. Engineering a system that could measure how such a process evolves on ultrashort timescales was extremely difficult. It has only recently become technically feasible.
Why local scientists and the world care
For the local research community in Würzburg this breakthrough represents years of work. The team is part of the Cluster of Excellence ctd.qmat. Postdoctoral researcher Siddhartha Dam explained that verifying the KPZ model in two dimensions took so long because these processes unfold on ultrashort timescales. The team succeeded in controlling a non equilibrium quantum system in the laboratory.
The KPZ framework has been applied to everything from crystal formation and population dynamics to flame fronts and even machine learning. This experimental confirmation strengthens the idea that very different systems may all follow the same hidden rules when they grow.
This milestone shows just how universal the growth model really is. It opens the door to understanding growth processes across physics, biology, and materials science with a single set of principles.
