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arXiv · 2412.07432

KPZ-like scaling on a high-dimensional hypersphere

Daniil Fedotov·Sergei Nechaev
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Abstract

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, $\gamma = 1/3$. In addition, we speculate about the topology of the orientational target space representing the surface of the hypersphere.

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Daniil Fedotov, Sergei Nechaev. 2024-12-10. KPZ-like scaling on a high-dimensional hypersphere. https://arxiv.org/abs/2412.07432

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