The Kardar-Parisi-Zhang exponents for the 2+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...
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doaj-58b7118492c54b8ca052841613c29aa82021-06-27T04:37:21ZengElsevierResults in Physics2211-37972021-07-0126104435The Kardar-Parisi-Zhang exponents for the 2+1 dimensionsMárcio S. Gomes-Filho0André L.A. Penna1Fernando A. Oliveira2Instituto de Física, Universidade de Brasília, Brasília-DF, BrazilInstituto de Física, Universidade de Brasília, Brasília-DF, BrazilInstituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação, Rua Barão de Jeremoabo s/n, 40170-115 Salvador-BA, Brazil; Corresponding author.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.http://www.sciencedirect.com/science/article/pii/S2211379721005520KPZ equationGrowth phenomenaKPZ exponentsUniversality |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Márcio S. Gomes-Filho André L.A. Penna Fernando A. Oliveira |
spellingShingle |
Márcio S. Gomes-Filho André L.A. Penna Fernando A. Oliveira The Kardar-Parisi-Zhang exponents for the 2+1 dimensions Results in Physics KPZ equation Growth phenomena KPZ exponents Universality |
author_facet |
Márcio S. Gomes-Filho André L.A. Penna Fernando A. Oliveira |
author_sort |
Márcio S. Gomes-Filho |
title |
The Kardar-Parisi-Zhang exponents for the 2+1 dimensions |
title_short |
The Kardar-Parisi-Zhang exponents for the 2+1 dimensions |
title_full |
The Kardar-Parisi-Zhang exponents for the 2+1 dimensions |
title_fullStr |
The Kardar-Parisi-Zhang exponents for the 2+1 dimensions |
title_full_unstemmed |
The Kardar-Parisi-Zhang exponents for the 2+1 dimensions |
title_sort |
kardar-parisi-zhang exponents for the 2+1 dimensions |
publisher |
Elsevier |
series |
Results in Physics |
issn |
2211-3797 |
publishDate |
2021-07-01 |
description |
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. |
topic |
KPZ equation Growth phenomena KPZ exponents Universality |
url |
http://www.sciencedirect.com/science/article/pii/S2211379721005520 |
work_keys_str_mv |
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