Scattering of charged fermion to two-dimensional wormhole with constant axial magnetic flux

Abstract

Scattering of charged fermion with $(1+2)$-dimensional wormhole in the presence of constant axial magnetic flux is explored. By extending the class of fermionic solutions of the Dirac equation in the curved space of wormhole surface to include normal modes with real energy and momentum, we found a quantum selection rule for the scattering of fermion waves to the wormhole. The newly found {\it momentum-angular momentum relation} implies that only fermion with the quantized momentum $k=m^{\prime }/a\sqrt{q}$ can be transmitted through the hole. The allowed momentum is proportional to an effective angular momentum quantum number $m^{\prime }$ and inversely proportional to the radius of the throat of the wormhole $a$. Flux dependence of the effective angular momentum quantum number permits us to select fermions that can pass through according to their momenta. A conservation law is also naturally enforced in terms of the unitarity condition among the incident, reflected, and transmitted waves. The scattering involving quasinormal modes~(QNMs) of fermionic states in the wormhole is subsequently explored. It is found that the transmitted waves through the wormhole for all scenarios involving QNMs are mostly suppressed and decaying in time. In the case of QNMs scattering, the unitarity condition is violated but a more generic relation of the scattering coefficients is established. When the magnetic flux $\varphi =mhc/e$, i.e., quantized in units of the magnetic flux quantum $hc/e$, the fermion will tunnel through the wormhole with zero reflection.

arXiv comment18 pages, 7 figures

References in corpus (18)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering
• Gauge fields from strain in graphene
• Quantum field theory in curved graphene spacetimes, Lobachevsky geometry, Weyl symmetry, Hawking effect, and all that
• Graphene wormholes: A condensed matter illustration of Dirac fermions in curved space
• Bound states and decay times of fermions in a Schwarzschild black hole background
• The ringing wormholes
• Dirac Quasinormal modes of Schwarzschild black hole
• Pseudo-magnetic field in curved graphene
• Pauli equation for a charged spin particle on a curved surface in an electric and magnetic field
• Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space
• Charged fermion in $(1+2)$-dimensional wormhole with axial magnetic field
• Constructing spherically symmetric Einstein-Dirac systems with multiple spinors: Ansatz, wormholes and other analytical solutions
• Pseudo-magnetic field and effective spin-orbit interaction for a spin-1/2 particle confined to a curved surface
• Graphene wormhole trapped by external magnetic field
• Slowly damped quasinormal modes of the massive Dirac field in d-dimensional Tangherlini spacetime
• Quasinormal modes of Dirac spinors in the background of rotating black holes in four and five dimensions

Cited by in corpus (1)

• Rotation effects on the graphene wormhole energy levels