AUTHOR=dos Anjos Petrus H. R. , Gomes-Filho Márcio S. , Alves Washington S. , Azevedo David L. , Oliveira Fernando A. 

TITLE=The Fractal Geometry of Growth: Fluctuation–Dissipation Theorem and Hidden Symmetry

JOURNAL=Frontiers in Physics

VOLUME=Volume 9 - 2021

YEAR=2021

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.741590

DOI=10.3389/fphy.2021.741590

ISSN=2296-424X

ABSTRACT=Growth in crystals can  be  \textcolor{red}{ 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  \textcolor{red}{ 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 \red{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.