Diffusion in quantum geometry
Abstract
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is controlled by a multiscale fractional diffusion equation, and physically interpreted as a composite stochastic process. The simplest example is a fractional telegraph process, describing quantum spacetimes with a spectral dimension equal to 2 in the ultraviolet and monotonically rising to 4 towards the infrared. The general profile of the spectral dimension of the recently introduced multifractional spaces is constructed for the first time.
Keywords
Cite
@article{arxiv.1204.2550,
title = {Diffusion in quantum geometry},
author = {Gianluca Calcagni},
journal= {arXiv preprint arXiv:1204.2550},
year = {2012}
}
Comments
5 pages, 1 figure. v2: title slightly changed, discussion improved