Description of KPZ interface growth by stochastic Loewner evolution
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908936834121728 |
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| author | Shibasaki, Yusuke Kosaka |
| author_facet | Shibasaki, Yusuke Kosaka |
| contents | In this study, we investigate the relationship between the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) equation and the stochastic Loewner equation (SLE), which is a one parameter family of the conformal mappings involving stochasticity. The author shows the correspondence between 1D KPZ equation with height function $h(x,t)=(3t^2x+x^3)/6t$ and Loewner equation driven by a nonlinear stochastic process, wherein the 1D dynamics of interface growth is characterized by Loewner entropy $S_{Loew}\simeq-\ln{t/κ}$. These results were numerically verified with discussions in relation to the universality in non-equilibrium statistical physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03711 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Description of KPZ interface growth by stochastic Loewner evolution Shibasaki, Yusuke Kosaka Statistical Mechanics In this study, we investigate the relationship between the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) equation and the stochastic Loewner equation (SLE), which is a one parameter family of the conformal mappings involving stochasticity. The author shows the correspondence between 1D KPZ equation with height function $h(x,t)=(3t^2x+x^3)/6t$ and Loewner equation driven by a nonlinear stochastic process, wherein the 1D dynamics of interface growth is characterized by Loewner entropy $S_{Loew}\simeq-\ln{t/κ}$. These results were numerically verified with discussions in relation to the universality in non-equilibrium statistical physics. |
| title | Description of KPZ interface growth by stochastic Loewner evolution |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2604.03711 |