KPZ-like scaling on a high-dimensional hypersphere
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929622568927232 |
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| author | Fedotov, Daniil Nechaev, Sergei |
| author_facet | Fedotov, Daniil Nechaev, Sergei |
| contents | We consider the orientational diffusion controlled by the hyperspherical Laplacian, $\nabla^2_D$, on the surface of the $D$--dimensional hypersphere in the limit $D \to \infty$. We find that for stretched paths with lengths relatively short compared to the hypersphere's radius, the finite-size corrections in orientational correlations are controlled by the Kardar-Parisi-Zhang (KPZ) scaling exponent, $γ= 1/3$. In addition, we speculate about the topology of the orientational target space representing the surface of the hypersphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07432 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | KPZ-like scaling on a high-dimensional hypersphere Fedotov, Daniil Nechaev, Sergei Statistical Mechanics We consider the orientational diffusion controlled by the hyperspherical Laplacian, $\nabla^2_D$, on the surface of the $D$--dimensional hypersphere in the limit $D \to \infty$. We find that for stretched paths with lengths relatively short compared to the hypersphere's radius, the finite-size corrections in orientational correlations are controlled by the Kardar-Parisi-Zhang (KPZ) scaling exponent, $γ= 1/3$. In addition, we speculate about the topology of the orientational target space representing the surface of the hypersphere. |
| title | KPZ-like scaling on a high-dimensional hypersphere |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2412.07432 |