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arXiv · 1204.2550

Diffusion in quantum geometry

Gianluca Calcagni
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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.

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Gianluca Calcagni. 2012-08-15. Diffusion in quantum geometry. https://doi.org/10.1103/physrevd.86.044021

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