Year: 2000
Type: article
Abstract: Fractons are anyons classified into equivalence classes and they obey 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 [Formula: see text] 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.
Author: da Cruz
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949452005