From the Complex Ginzburg--Landau Equation to the Kardar--Parisi--Zhang Equation: A Hierarchical Relationship in the Light of Information Dynamics
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2026
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| _version_ | 1866901986059747328 |
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| author | Huang, Kai |
| author_facet | Huang, Kai |
| contents | <pre>The Kardar–Parisi–Zhang (KPZ) equation describes universal scaling behaviour in a wide variety of non-equilibrium interface growth systems, while the complex Ginzburg–Landau (CGL) equation governs the spatiotemporal evolution of a complex order parameter and serves as the core mathematical vehicle of the Information Dynamics framework. In this work we first <strong>derive the KPZ equation directly from the CGL equation</strong> by performing an amplitude–phase decomposition in regions where the amplitude is approximately constant, mapping the phase fluctuations onto a height field, and identifying the nonlinear term that emerges from the quartic potential of the CGL equation. Explicit microscopic expressions are obtained for all KPZ coefficients. We then review recent independent advances in this field—the numerical verification of CGL-to-KPZ universality by Vercesi et al. (2024) and the rigorous probabilistic proof by Yang (2025). Based on our derivation and these converging lines of evidence, we discuss the hierarchical relationship between the two equations: the CGL equation, which operates on a complex order parameter and naturally encodes both amplitude and phase information, is the more fundamental dynamical description; the KPZ equation is its compressed projection in the particular limit of interface growth. This viewpoint offers a deeper insight into why the KPZ universality class is so robust, and it connects the recent experimental verification of two‑dimensional KPZ scaling with the broader theoretical framework of complex field dynamics.</pre> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20248700 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | From the Complex Ginzburg--Landau Equation to the Kardar--Parisi--Zhang Equation: A Hierarchical Relationship in the Light of Information Dynamics Huang, Kai Information Dynamics KPZ equation <pre>The Kardar–Parisi–Zhang (KPZ) equation describes universal scaling behaviour in a wide variety of non-equilibrium interface growth systems, while the complex Ginzburg–Landau (CGL) equation governs the spatiotemporal evolution of a complex order parameter and serves as the core mathematical vehicle of the Information Dynamics framework. In this work we first <strong>derive the KPZ equation directly from the CGL equation</strong> by performing an amplitude–phase decomposition in regions where the amplitude is approximately constant, mapping the phase fluctuations onto a height field, and identifying the nonlinear term that emerges from the quartic potential of the CGL equation. Explicit microscopic expressions are obtained for all KPZ coefficients. We then review recent independent advances in this field—the numerical verification of CGL-to-KPZ universality by Vercesi et al. (2024) and the rigorous probabilistic proof by Yang (2025). Based on our derivation and these converging lines of evidence, we discuss the hierarchical relationship between the two equations: the CGL equation, which operates on a complex order parameter and naturally encodes both amplitude and phase information, is the more fundamental dynamical description; the KPZ equation is its compressed projection in the particular limit of interface growth. This viewpoint offers a deeper insight into why the KPZ universality class is so robust, and it connects the recent experimental verification of two‑dimensional KPZ scaling with the broader theoretical framework of complex field dynamics.</pre> |
| title | From the Complex Ginzburg--Landau Equation to the Kardar--Parisi--Zhang Equation: A Hierarchical Relationship in the Light of Information Dynamics |
| topic | Information Dynamics KPZ equation |
| url | https://doi.org/10.5281/zenodo.20248700 |