KPZ-like scaling on a high-dimensional hypersphere

TL;DR

This paper investigates the scaling behavior of orientational diffusion on high-dimensional hyperspheres, revealing KPZ-like scaling in finite-size corrections and discussing the topology of the target space.

Contribution

It demonstrates KPZ-like scaling in orientational correlations on high-dimensional hyperspheres and explores the topology of the orientational target space.

Findings

Finite-size corrections follow KPZ scaling exponent $rac{1}{3}$.

Scaling behavior observed for short paths relative to hypersphere radius.

Discussion on the topology of the hypersphere's surface as an orientational space.

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.