Diffusion in kappa deformed space and Spectral Dimension

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 $k\ge 0$ and $-\infty$ for $k<0$ at high energies .

12 Pages, 2 Figures