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Diffusion in quantum geometry · Around

2012

Diffusion in quantum geometry

Calcagni, Gianluca

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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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Then

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Later among the works it cites.
G. Calcagni, Phys. Rev. Lett. 104
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H. Allouba and W. Zheng, Ann. Probab. 29
2011
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A. Connes, J. High Energy Phys. 11 (2006) 081 ; D. Benedetti, Phys. Rev. Lett. 102
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G. Calcagni, Phys. Rev. D 84
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