article · 1999

Modular group

Caixa Postal, Typeset Using Revtex

Cited by 0Abstract and details only

Abstract

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 ˜ h = 3 −h shows us that the filling factors for which the FQHE were observed just appears 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.

Cite this paper

APA 7

Postal, C., & Revtex, T. U. (1999). Modular group.

MLA 9

Postal, Caixa, and Typeset Using Revtex. “Modular group.” 1999.

Chicago

Postal, Caixa, and Typeset Using Revtex. 1999. “Modular group.”

Harvard

Postal, C. and Revtex, T.U. (1999) ‘Modular group’.

BibTeX

@article{postal1999modular,
  title = {{Modular group}},
  author = {Postal, Caixa and Revtex, Typeset Using},
  year = {1999}
}

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