Wurzburg team confirms 40-year-old Kardar-Parisi-Zhang growth law in two dimensions using exciton-polariton condensates

Overview

A team led by the University of Wurzburg has produced the first experimental demonstration of Kardar-Parisi-Zhang (KPZ) universal scaling in two dimensions, closing a forty-year gap between a celebrated piece of statistical physics and the laboratory. The result, reported by ScienceDaily and Phys.org, was published in Science on April 9, 2026 with DOI 10.1126/science.aeb4154, according to SciTechDaily.

The KPZ equation was introduced in 1986 to describe how rough surfaces grow in time when noise and nonlinearity dominate the dynamics. Experimentalists confirmed it in one-dimensional systems in 2022, but the two-dimensional case — which corresponds to most physical surfaces — had remained out of reach until now.

What the experiment measured

The Wurzburg group used a gallium arsenide (GaAs) semiconductor heterostructure fabricated by molecular beam epitaxy, with mirror layers that confine photons inside a thin quantum film, as Phys.org reports. When the sample is cooled to -269.15 C and continuously pumped with a laser, polaritons — hybrid quasiparticles of photons and excitons — form in the film. The polaritons exist only out of equilibrium and decay within a few picoseconds, according to ScienceDaily.

The team imaged the spatial and temporal evolution of these polaritons across a sample roughly 20 micrometers across, as SciTechDaily describes. “We can precisely track where the polaritons are in the material,” Siddhartha Dam, a postdoctoral researcher at the Wurzburg-Dresden Cluster of Excellence ctd.qmat, told ScienceDaily.

The authors’ arXiv preprint summarises the result by saying the measurements “reveal correlation dynamics and scaling exponents in excellent agreement with 2D KPZ predictions,” using spectroscopy and interferometry on exciton-polariton condensates driven at varying conditions.

Why a 2D confirmation matters

KPZ scaling is a universality class: very different physical systems are predicted to follow the same statistical laws once one rescales space and time. “When surfaces grow — whether crystals, bacteria, or flame fronts — the process is always nonlinear and random,” Dam said, describing the breadth of phenomena the equation is supposed to govern.

The theoretical groundwork for applying KPZ to driven-dissipative quantum condensates was laid in 2015 by Sebastian Diehl of the University of Cologne, who is a co-author of the new study, Phys.org notes. “The experimental demonstration of KPZ universality in two-dimensional material systems highlights just how fundamental this equation is for real non-equilibrium systems,” Diehl told Phys.org.

Dam framed the broader achievement in similar terms. “We have now succeeded in controlling a non-equilibrium quantum system in the laboratory,” he said in Phys.org’s coverage.

The 2026 result extends the chain begun by a Paris-based group that, in 2022, confirmed KPZ scaling in a one-dimensional polariton system. Two dimensions are mathematically harder and physically more relevant: most everyday surfaces — crystal facets, bacterial colonies, propagating fronts — are extended in two spatial directions. The arXiv abstract argues the work “establishes exciton-polariton condensates as a platform for studying nonequilibrium quantum systems,” per the preprint.

What we don’t know

The paper measures KPZ exponents in a specific GaAs platform under specific drive conditions; it does not yet confirm that other 2D systems predicted to fall in the same universality class — spin chains, fluid interfaces, biological growth fronts — will share the same exponents under experimental scrutiny. The published Science article is at DOI 10.1126/science.aeb4154 (volume 392, page 221), as listed by ScienceDaily, but technical details such as exponent values and confidence intervals require reading the paper itself.

The authors and outlets cited above also do not claim immediate practical applications; the work is positioned as foundational physics rather than as a step toward a device.