Diffusion in κ-deformed space and spectral dimension

Abstract

In this paper, we derive the expression for spectral dimension using a modified diffusion equation in the [Formula: see text]-deformed spacetime. We start with the Beltrami–Laplace operator in the [Formula: see text]-Minkowski spacetime 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 “[Formula: see text]” and also on an integer “[Formula: see text]”, apart from the topological dimension. Using this, we show that, for large diffusion times the spectral dimension approaches the usual topological dimension whereas spectral dimension diverges to [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text] at high energies.