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arXiv · 1009.3267

Hausdorff dimension of a particle path in a quantum manifold

Piero Nicolini·Benjamin Niedner
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Abstract

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.

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Piero Nicolini, Benjamin Niedner. 2011-01-14. Hausdorff dimension of a particle path in a quantum manifold. https://doi.org/10.1103/physrevd.83.024017

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