The fractal geometry of growth: fluctuation-dissipation theorem and hidden symmetry

Abstract

Growth in crystals can be { usually } described by field equations such as the Kardar-Parisi-Zhang (KPZ) equation. While the crystalline structure can be characterized by Euclidean geometry with its peculiar symmetries, the growth dynamics creates a fractal structure at the interface of a crystal and its growth medium, which in turn determines the growth. Recent work (The KPZ exponents for the 2+ 1 dimensions, MS Gomes-Filho, ALA Penna, FA Oliveira; \textit{Results in Physics}, 104435 (2021)) associated the fractal dimension of the interface with the growth exponents for KPZ, and provides explicit values for them. In this work we discuss how the fluctuations and the responses to it are associated with this fractal geometry and the new hidden symmetry associated with the universality of the exponents.

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Cited by in corpus (6)

• Universal scaling relation for growth phenomena
• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Restoring the fluctuation-dissipation theorem in Kardar-Parisi-Zhang universality class through a new emergent fractal dimension
• A geometrical interpretation of critical exponents
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• Scaling, Fractal Dynamics and Critical Exponents: Application in a non-integer dimensional Ising model