Direct Evidence for Universal Statistics of Stationary Kardar-Parisi-Zhang Interfaces

Abstract

The nonequilibrium steady state of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class is studied in-depth by exact solutions, yet no direct experimental evidence of its characteristic statistical properties has been reported so far. This is arguably because, for an infinitely large system, infinitely long time is needed to reach such a stationary state and also to converge to the predicted universal behavior. Here we circumvent this problem in the experimental system of growing liquid-crystal turbulence, by generating an initial condition that possesses a long-range property expected for the KPZ stationary state. The resulting interface fluctuations clearly show characteristic properties of the 1D stationary KPZ interfaces, including the convergence to the Baik-Rains distribution. We also identify finite-time corrections to the KPZ scaling laws, which turn out to play a major role in the direct test of the stationary KPZ interfaces. This paves the way to explore unsolved properties of the stationary KPZ interfaces experimentally, making possible connections to nonlinear fluctuating hydrodynamics and quantum spin chains as recent studies unveiled relation to the stationary KPZ.

6+3 pages, 4+3 figures; published version

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Cited by in corpus (9)

• The KPZ equation in a half space with flat initial condition and the unbinding of a directed polymer from an attractive wall
• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains
• Half-space stationary Kardar-Parisi-Zhang equation beyond the Brownian case
• Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation
• KPZ fluctuations in finite volume
• Initial perturbation matters: implications of geometry-dependent universal Kardar-Parisi-Zhang statistics for spatiotemporal chaos
• Phase diagram and universal scaling regimes of two-dimensional exciton-polariton Bose-Einstein condensates
• Universality in many-body driven systems with an umbilic point
• The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation