On the dual topological quantum numbers filling factors

Physics – Condensed Matter – Mesoscale and Nanoscale Physics

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Typos corrected, references added and updated, 8 pages, latex. Comments on paper W. Pan et al, Phys. Rev. Lett. {\bf 90}, 0168

Scientific paper

We consider recent experimental results [W. Pan {\it et al}, Phys. Rev. Lett. {\bf 90}, 016801 (2003)] for occurrence of the fractional quantum Hall effect-FQHE under the perspective of our formulation in terms of {\it fractons}. These objects carry rational or irrational values of spin and satisfy a {\it fractal distribution function} associated with a {\it fractal von Neumann entropy}. According to our approach the {\it FQHE occurs in pairs of dual topological quantum numbers fillings factors} and this geometrical character comes from the {\it connection betwenn the fractal parameter or Hausdorff dimension $h$ and the spin $s$ of the particles}. We suggest to the experimentalists consider our ideas and verify in fact that this phenomenon of FQHE satisfy a {\it symmetry principle} discovered by us, i.e, {\it the duality symmetry betwenn universal classes of fractons}.

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