A quantum-geometrical description of fracton statistics

Details A quantum-geometrical description of fracton statistics A quantum-geometrical description of fracton statistics

2002-12-23

arxiv.org/abs/cond-mat/0212567v5

International Journal of Modern Physics A18 (2003), 2213-2219

Physics

Condensed Matter

Statistical Mechanics

Typos corrected, latex, 8 pages, Talk given at the 2nd International Londrina Winter School: Mathematical Methods in Physics,

Scientific paper

10.1142/S0217751X03015672

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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