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Creation of planar charged fermions in Coulomb and Aharonov–Bohm potentials

  • V. R. KhalilovEmail author
Regular Article - Theoretical Physics

Abstract

The creation of charged fermions from the vacuum by a Coulomb field in the presence of an Aharonov–Bohm (AB) potential are studied in 2+1 dimensions. The process is governed by a (singular) Dirac Hamiltonian that requires the supplementary definition in order for it to be treated as a self-adjoint quantum-mechanical operator. By constructing a one-parameter self-adjoint extension of the Dirac Hamiltonian, specified by boundary conditions, we describe the (virtual bound) quasistationary states with “complex energy” emerging in an attractive Coulomb potential, derive for the first time, complex equations (depending upon the electron spin and the extension parameter) for the quasistationary state “complex energy”. The constructed self-adjoint Dirac Hamiltonians in Coulomb and AB potentials are applied to provide a correct description to the low-energy electron excitations, as well as the creation of charged quasiparticles from the vacuum in graphene by the Coulomb impurity in the presence of AB potential. It is shown that the strong Coulomb field can create charged fermions for some range of the extension parameter.

Keywords

Coulomb Field Charged Fermion Quasistationary State Physical Sheet Lower Continuum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The author is grateful to K.E. Lee for the help with the numerical calculations.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Faculty of PhysicsMoscow State UniversityMoscowRussia

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