Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation

Bao-Xing Xie; Kang Xue; Mo-Lin Ge

doi:10.1103/PhysRevA.77.064101

Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation

Quantum Physics 2009-11-13 v2

Authors: Bao-Xing Xie , Kang Xue , Mo-Lin Ge

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Abstract

In this paper we discuss a new type of 4-dimensional representation of the braid group. The matrices of braid operations are constructed by q-deformation of Hamiltonians. One is the Dirac Hamiltonian for free electron with mass m, the other, which we find, is related to the Bogoliubov Hamiltonian for quasiparticles in $^3$ He-B with the same free energy and mass being m/2. In the process, we choose the free q-deformation parameter as a special value in order to be consistent with the anyon description for fractional quantum Hall effect with $\nu = 1/2$ .

Keywords

braid group bogoliubov hamiltonian dirac hamiltonian q-deformation anyon fractional quantum hall effect helium-3

Cite

@article{arxiv.0711.3260,
  title  = {Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation},
  author = {Bao-Xing Xie and Kang Xue and Mo-Lin Ge},
  journal= {arXiv preprint arXiv:0711.3260},
  year   = {2009}
}

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3 pages, 5 figures

Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation

Abstract

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