Diffusion in multiscale spacetimes
High Energy Physics - Theory
2015-03-20 v2 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are partly based on the literature in probability and percolation theory but their physical interpretation here is different since they apply to quantum spacetime itself. The case of multiscale (in particular, multifractal) spacetimes is then considered through a number of examples and the most general spectral-dimension profile of multifractional spaces is constructed.
Cite
@article{arxiv.1205.5046,
title = {Diffusion in multiscale spacetimes},
author = {Gianluca Calcagni},
journal= {arXiv preprint arXiv:1205.5046},
year = {2015}
}
Comments
23 pages, 5 figures. v2: discussion improved, typos corrected, references added