The Hausdorff dimension of fractal sets and fractional quantum Hall effect

Abstract

We consider Farey series of rational numbers in terms of {\it fractal sets} labeled by the Hausdorff dimension with values defined in the interval 1$<$$h$$<$$2$ and associated with fractal curves. Our results come from the observation that the fractional quantum Hall effect-FQHE occurs in pairs of {\it dual topological quantum numbers}, the filling factors. These quantum numbers obey some properties of the Farey series and so we obtain that {\it the universality classes of the quantum Hall transitions are classified in terms of $h$}. The connection between Number Theory and Physics appears naturally in this context.

Typos corrected, 8 pages, latex. To appear in Chaos, Solitons and Fractals, 2003

Cited by in corpus (1)

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