Diffusion in quantum geometry

Gianluca Calcagni
Phys. Rev. D 86, 044021 – Published 15 August 2012

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.

  • Figure
  • Received 11 April 2012

DOI:https://doi.org/10.1103/PhysRevD.86.044021

© 2012 American Physical Society

Authors & Affiliations

Gianluca Calcagni

  • Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Golm, Germany

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Issue

Vol. 86, Iss. 4 — 15 August 2012

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