Journal
RESULTS IN PHYSICS
Volume 26, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.rinp.2021.104435
Keywords
KPZ equation; Growth phenomena; KPZ exponents; Universality
Funding
- Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) [CNPq312497/2018-0]
- Fundacao de Apoio a Pesquisa do Distrito Federal (FAPDF) [FAPDF00193-00000120/2019-79]
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This study connects growth exponents with the fractal dimension of rough interfaces using physical and geometric analysis, determining the growth exponents for 2+1 dimensions and suggesting the nonexistence of an upper critical dimension in d+1 dimensions.
The Kardar-Parisi-Zhang (KPZ) equation has been connected to a large number of important stochastic processes in physics, chemistry and growth phenomena, ranging from classical to quantum physics. The central quest in this field is the search for ever more precise universal growth exponents. Notably, exact growth exponents are only known for 1+1 dimensions. In this work, we present physical and geometric analytical methods that directly associate these exponents to the fractal dimension of the rough interface. Based on this, we determine the growth exponents for the 2+1 dimensions, which are in agreement with the results of thin films experiments and precise simulations. We also make a first step towards a solution in d+1 dimensions, where our results suggest the inexistence of an upper critical dimension.
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