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 momentum–angular momentum relation implies that only fermion with the quantized momentum k=m'/asqrt{q} can be transmitted through the hole. The allowed momentum is proportional to an effective angular momentum quantum number m' 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 phi =mhc/e, i.e., quantized in units of the magnetic flux quantum hc/e, the fermion will tunnel through the wormhole with zero reflection.