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Sinc noise for the Kardar-Parisi-Zhang equation
Oliver Niggemann1, Haye Hinrichsen1
1Fakultät für Physik und Astronomie, Universität Würzburg, 97074 Würzburg, Germany.
Physical Review. E
|July 18, 2018
Summary
The Kardar-Parisi-Zhang (KPZ) equation with spatially correlated noise exhibits universal dynamics. Finite correlation length in the noise, regardless of its specific profile, leads to behavior indistinguishable from uncorrelated white noise at large scales.
Area of Science:
- Statistical Physics
- Nonlinear Dynamics
- Condensed Matter Physics
Background:
- The Kardar-Parisi-Zhang (KPZ) equation models the dynamics of interfaces and surfaces.
- Understanding the effect of noise correlations on KPZ universality is crucial.
- Previous studies explored Gaussian noise, but sinc noise remains less understood.
Purpose of the Study:
- To investigate the impact of spatially correlated sinc noise on the one-dimensional KPZ equation.
- To analyze the role of the noise correlation length (ξ) in KPZ dynamics.
- To determine if KPZ dynamics exhibit universality with respect to finite correlation lengths.
Main Methods:
- Field-theoretic dynamic renormalization-group techniques.
- Analysis of sinc noise profile in Fourier space with correlation length ξ.
- Comparison with existing results for Gaussian noise.
Main Results:
- The large-scale behavior of the KPZ equation with sinc noise is governed by the standard KPZ fixed point.
- Finite correlation length ξ in sinc noise leads to dynamics equivalent to pure white noise.
- This finding aligns with previous results for Gaussian noise, suggesting a broader universality.
Conclusions:
- KPZ dynamics demonstrate universality concerning the specific structure of spatially correlated noise.
- The universality holds as long as the noise correlation length (ξ) is finite.
- This implies robustness of KPZ universality class to different finite-range correlations.
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