Fractons and Fractal Statistics
| dc.creator | da Cruz, Wellington | |
| dc.date | 1999-05-31 | |
| dc.date | 2000-07-31 | |
| dc.date.accessioned | 2026-07-07T11:48:14Z | |
| dc.date.available | 2026-07-07T11:48:14Z | |
| dc.description | Fractons are anyons classified into equivalence classes and they obey a specific fractal statistics. The equivalence classes are labeled by a fractal parameter or Hausdorff dimension $h$. We consider this approach in the context of the Fractional Quantum Hall Effect (FQHE) and the concept of duality between such classes, defined by $\tilde{h}=3-h$ shows us that the filling factors for which the FQHE were observed just appear into these classes. A connection between equivalence classes $h$ and the modular group for the quantum phase transitions of the FQHE is also obtained. A $β-$function is defined for a complex conductivity which embodies the classes $h$. The thermodynamics is also considered for a gas of fractons $(h,ν)$ with a constant density of states and an exact equation of state is obtained at low-temperature and low-density limits. We also prove that the Farey sequences for rational numbers can be expressed in terms of the equivalence classes $h$. | |
| dc.description | 25pages, latex, additional references. To appear in International Journal of Modern Physics A (2000) | |
| dc.identifier | https://arxiv.org/abs/hep-th/9905229 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9905229 | |
| dc.identifier | Int.J.Mod.Phys.A15:3805-3828,2000 | |
| dc.identifier | doi:10.1016/S0217-751X(00)00231-5 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/202851 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Chaotic Dynamics | |
| dc.subject | Condensed Matter | |
| dc.title | Fractons and Fractal Statistics | |
| dc.type | text |