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A quantum-geometrical description of fracton statistics

Wellington da Cruz
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Abstract

We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution function associated with a fractal von Neumann entropy. Fractons are charge-flux systems defined in two-dimensional multiply connected space and they carry rational or irrational values of spin. This formulation can be considered in the context of the fractional quantum Hall effect-FQHE and number theory.

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Wellington da Cruz. 2003-05-26. A quantum-geometrical description of fracton statistics. https://doi.org/10.1142/s0217751x03015672

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