2D Quasiparticle Array Confirms Universal Scaling Theory

Researchers from the Würzburg–Dresden Cluster of Excellence (ctd.qmat) have provided the first experimental proof of Kardar-Parisi-Zhang (KPZ) universality in a two-dimensional system. The findings, published in April 2026, demonstrate a universal law governing random fluctuations in systems operating out of thermodynamic equilibrium.

The study utilized a semiconductor sample approximately 20 micrometers in size to observe the nonlinear and random growth of surfaces, and interfaces. This achievement marks the first time KPZ universality has been demonstrated in a system spanning two dimensions in both space and time.

The KPZ Equation and Non-Equilibrium Dynamics

The Kardar-Parisi-Zhang equation is a mathematical framework established by three physicists in 1986. It is designed to describe how boundaries grow and evolve in systems that are driven away from thermal equilibrium, characterized by continuous energy input and nonlinear development.

While the theoretical foundation was set decades ago, experimental verification has been gradual. The model was first confirmed for one-dimensional systems in 2022 by a research group located in Paris. However, evidence for the theory in two-dimensional systems had previously remained elusive.

The Role of Polaritons in Quantum Growth

To verify the theory in two dimensions, the research team used an engineered gallium arsenide semiconductor. By continuously exciting this semiconductor with a laser, the scientists created polaritons.

Polaritons are hybrid quasiparticles formed by the coupling of photons, which are particles of light, and excitons, which are particles of matter. These quasiparticles are highly dynamic and only exist under non-equilibrium conditions.

The use of polaritons allowed the researchers to precisely track the growth and decay of the non-equilibrium system in real time. The experimental setup involved a 2D array of exciton-polariton condensates that emerged within an array of semiconductor micropillars.

Development and Research Contributions

The conceptual approach of testing a universal growth theory within a quantum system using polaritons was developed by Sebastian Diehl. Diehl is a professor at the Institute for Theoretical Physics at the University of Cologne and a member of the research team.

By utilizing these quantum fluids of light, the team was able to observe KPZ scaling in the 2D array, confirming that the mathematical framework accurately captures the complex spatial and temporal evolution of growing boundaries in such systems.

Scientific Context of Universal Scaling

Universal scaling refers to the observation that very different physical systems can exhibit the same behavior when viewed at a certain scale, regardless of their specific microscopic details. In this case, the KPZ equation provides a universal law for random fluctuations across different types of growing interfaces.

The verification of this law in a 2D quantum system expands the understanding of non-equilibrium dynamics. These dynamics are essential for understanding any system where energy is constantly being added and the system does not settle into a stable, thermal equilibrium.