Diffusion in kappa deformed space and Spectral Dimension

TL;DR

This paper derives a modified spectral dimension in kappa-deformed space-time using a deformed diffusion equation, revealing how it varies with deformation parameters and energy scales, and approaches classical dimensions at large diffusion times.

Contribution

It introduces a new formulation of spectral dimension in kappa-Minkowski space-time based on a modified diffusion equation, highlighting the effects of deformation parameters.

Findings

Spectral dimension depends on deformation parameter and integer k.

At large diffusion times, spectral dimension approaches the topological dimension.

Spectral dimension diverges at high energies for certain parameter values.

Abstract

In this paper, we derive the expression for spectral dimension using a modified diffusion equation in the kappa-deformed space-time. We start with the Beltrami-Laplace operator in the kappa-Minkowski space-time and obtain the deformed diffusion equation. From the solution of this deformed diffusion equation, we calculate the spectral dimension which depends on the deformation parameter `$a$' and also on an integer `$k$', apart from the topological dimension. Using this, we show that, for large diffusion times the spectral dimension approaches the usual topological dimension where as spectral dimension diverges to $+\infty$ for $k\geq 0$ and $-\infty$ for $k < 0$ at high energies .