Fractal sets of dual topological quantum numbers
| dc.creator | da Cruz, Wellington | |
| dc.date | 2003-06-27 | |
| dc.date | 2004-06-18 | |
| dc.date.accessioned | 2026-07-07T04:30:19Z | |
| dc.date.available | 2026-07-07T04:30:19Z | |
| dc.description | The universality classes of the quantum Hall transitions are considered in terms of fractal sets of dual topological quantum numbers filling factors, labelled by a fractal or Hausdorff dimension defined into the interval $1 < h < 2$ and associated with fractal curves. We show that our approach to the fractional quantum Hall effect-FQHE is free of any empirical formula and this characteristic appears as a crucial insight for our understanding of the FQHE. According to our formulation, the FQHE gets a fractal structure from the connection between the filling factors and the Hausdoff dimension of the quantum paths of particles termed fractons which obey a fractal distribution function associated with a fractal von Neumann entropy. This way, the quantum Hall transitions satisfy some properties related to the Farey sequences of rational numbers and so our theoretical description of the FQHE establishes a connection between physics, fractal geometry and number theory. The FQHE as a convenient physical system for a possible prove of the Riemann hypothesis is suggested. | |
| dc.description | Misprints corrected. Latex, 15 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0306071 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0306071 | |
| dc.identifier | Published in "FOCUS ON MATHEMATICAL PHYSICS RESEARCH", ed. by C. V. Benton (Nova Science Publishers, Inc) (2004), pp.177-192.) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57430 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Number Theory | |
| dc.title | Fractal sets of dual topological quantum numbers | |
| dc.type | text |