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

TL;DR

This paper investigates the creation of charged fermions from vacuum in 2+1 dimensions under Coulomb and Aharonov-Bohm potentials, using self-adjoint extensions of the Dirac Hamiltonian to describe quasistationary states and particle creation.

Contribution

It introduces a novel method of defining self-adjoint Dirac Hamiltonians with boundary conditions to analyze quasistationary states and particle creation in combined Coulomb and AB potentials.

Findings

Charged fermions can be created by strong Coulomb fields within certain parameters.

Derived complex equations for quasistationary state energies depending on spin and boundary conditions.

Provided a consistent quantum-mechanical description of electron excitations and vacuum polarization in graphene-like systems.

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.