Restoring the fluctuation-dissipation theorem in Kardar-Parisi-Zhang universality class through a new emergent fractal dimension
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arXiv
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2024
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| author | Gomes-Filho, Márcio S. de Castro, Pablo Liarte, Danilo B. Oliveira, Fernando A. |
| author_facet | Gomes-Filho, Márcio S. de Castro, Pablo Liarte, Danilo B. Oliveira, Fernando A. |
| contents | The Kardar-Parisi-Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height probability distributions; the search for ever more precise universal growth exponents; and the apparent absence of a fluctuation-dissipation theorem (FDT) for spatial dimension $d>1$. Notably, these questions were answered exactly only for $1+1$ dimensions. In this work, we propose a new FDT valid for the KPZ problem in $d+1$ dimensions. This is done by rearranging terms and identifying a new correlated noise which we argue to be characterized by a fractal dimension $d_n$. We present relations between the KPZ exponents and two emergent fractal dimensions, namely $d_f$, of the rough interface, and $d_n$. Also, we simulate KPZ growth to obtain values for transient versions of the roughness exponent $α$, the surface fractal dimension $d_f$ and, through our relations, the noise fractal dimension $d_n$. Our results indicate that KPZ may have at least two fractal dimensions and that, within this proposal, a FDT is restored. Finally, we provide new insights into the old question about the upper critical dimension of the KPZ universality class. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_15576 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restoring the fluctuation-dissipation theorem in Kardar-Parisi-Zhang universality class through a new emergent fractal dimension Gomes-Filho, Márcio S. de Castro, Pablo Liarte, Danilo B. Oliveira, Fernando A. Statistical Mechanics The Kardar-Parisi-Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height probability distributions; the search for ever more precise universal growth exponents; and the apparent absence of a fluctuation-dissipation theorem (FDT) for spatial dimension $d>1$. Notably, these questions were answered exactly only for $1+1$ dimensions. In this work, we propose a new FDT valid for the KPZ problem in $d+1$ dimensions. This is done by rearranging terms and identifying a new correlated noise which we argue to be characterized by a fractal dimension $d_n$. We present relations between the KPZ exponents and two emergent fractal dimensions, namely $d_f$, of the rough interface, and $d_n$. Also, we simulate KPZ growth to obtain values for transient versions of the roughness exponent $α$, the surface fractal dimension $d_f$ and, through our relations, the noise fractal dimension $d_n$. Our results indicate that KPZ may have at least two fractal dimensions and that, within this proposal, a FDT is restored. Finally, we provide new insights into the old question about the upper critical dimension of the KPZ universality class. |
| title | Restoring the fluctuation-dissipation theorem in Kardar-Parisi-Zhang universality class through a new emergent fractal dimension |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2402.15576 |