论文标题
生长的分形几何形状：波动散文定理和隐藏对称性
The fractal geometry of growth: fluctuation-dissipation theorem and hidden symmetry
论文作者
论文摘要
晶体中的生长可以由诸如Kardar-Parisi-Zhang（KPZ）方程之类的场方程描述。虽然晶体结构的特征是欧几里得的几何形状具有其特殊的对称性，但生长动力学在晶体及其生长培养基的界面上产生了分形结构，从而决定了生长。最近的工作（2+ 1维度的KPZ指数，MS Gomes-Filho，Ala Penna，fa oliveira; \ textit {in theck in Physics}，104435（2021））将界面的分形维度与KPZ的生长经费相关联，并为其提供了explacitiit and Forexlapen。在这项工作中，我们讨论了波动及其对其的响应如何与该分形几何形状以及与指数通用性相关的新隐藏对称性相关联。
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.
