2010/09/30 by Piero Nicolini, Benjamin Niedner · 2 citations
Physics and Astronomy · #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.83.024017
published as Phys.Rev.D83:024017,2011 · 7 pages, 4 figure, updated version which matches that published on Physical Review D
arxiv created 2011/01/14 · arxiv updated 2011/01/26
After recalling the concept of the Hausdorff dimension, we study the fractal properties of a quantum particle path. As a novelty we consider the possibility for the space where the particle propagates to be endowed with a quantum-gravity-induced minimal length. We show that the Hausdorff dimension accounts for both the quantum mechanics uncertainty and manifold fluctuations. In addition the presence of a minimal length breaks the self-similarity property of the erratic path of the quantum particle. Finally we establish a universal property of the Hausdorff dimension as well as the spectral dimension: They both depend on the amount of resolution loss which affects both the path and the manifold when quantum gravity fluctuations occur.