393 research outputs found
Creation of planar charged fermions in Coulomb and Aharonov-Bohm potentials
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.Comment: 10 pages, 3 figures. arXiv admin note: substantial text overlap with
arXiv:1305.204
Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field
The polarization operator (tensor) for planar charged fermions in constant
uniform magnetic field is calculated in the one-loop approximation of the 2+1
dimensional quantum electrodynamics (QED) with a nonzero fermion
density. We construct the Green function of the Dirac equation with a constant
uniform external magnetic field in the QED at the finite chemical
potential, find the imaginary part of this Green function and then obtain the
polarization tensor related to the combined contribution from real particles
occupying the finite number of energy levels and magnetic field. We expect that
some physical effects under consideration seem to be likely to be revealed in a
monolayer graphene sample in the presence of external constant uniform magnetic
field perpendicular to it.Comment: 9 pages, 2 references are delete
Plane density of induced vacuum charge in a supercritical Coulomb potential
An expression for the density of a planar induced vacuum charge is obtained
in a strong Coulomb potential in coordinate space. Treatment is based on a
self-adjoint extension approach for constructing of the Green's function of a
charged fermion in this potential. Induced vacuum charge density is calculated
and analyzed at the subcritical and supercritical Coulomb potentials for
massless and massive fermions. The behavior of the obtained vacuum charge
density is investigated at long and short distances from the Coulomb center.
The induced vacuum charge has a screening sign. Screening of a Coulomb impurity
in graphene is briefly discussed. We calculate the real vacuum polarization
charge density that acquires the quantum electrodynamics vacuum in the
supercritical Coulomb potential due to the so-called real vacuum polarization.
It is shown that the vacuum charge densities essentially differ in massive and
massless cases. We expect that our results can, as a matter of principle, be
tested in graphene with a supercritical Coulomb impurity.Comment: 12 pages. arXiv admin note: substantial text overlap with
arXiv:1601.0766
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