Abstract
We investigate the effects of magnetic field on a charged fermion in a (1+2)-dimensional wormhole. Applying external magnetic field along the axis direction of the wormhole, the Dirac equation is set up and analytically solved in two scenarios, constant magnetic flux and constant magnetic field through the throat of the wormhole. For the constant magnetic flux scenario, the system can be solved analytically and exact solutions are found. For the constant magnetic field scenario, with the short wormhole approximation, the quantized energies and eigenstates are obtained. The system exhibits both the spin-orbit coupling and the Landau quantization for the stationary states in both scenarios. The intrinsic curvature of the surface induces the spin-orbit and spin-magnetic Landau couplings that generate imaginary energy. Imaginary energy can be interpreted as the energy dissipation and instability of the states. Generically, the states of charged fermion in wormhole are quasinormal modes (QNMs) that could be unstable for positive imaginary frequencies and decaying for negative imaginary ones. For the constant flux scenario, the fermions in the wormhole can behave like bosons and have arbitrary statistics depending on the flux. We also discuss the implications of our results in the graphene wormholesystem.
Highlights
Applying gauge field to the constrained quantum particles can generate curious effects
Even when the particle moves in the region with zero field, it can still experience phase shift when travelled around the non-zero field region, i.e., the Aharonov– Bohm (AB) effect [10]
Quantum Hall effects are notably an example of profound phenomena emerging in the constrained fermionic system with external gauge fields
Summary
Applying gauge field to the constrained quantum particles can generate curious effects. The AB effect occurs when the charged particles are confined to a surface such as the nanotube [11]. Graphene is an ideal place to study behaviour of confined charged fermions such as electrons in a two-dimensional surface since its thickness is only roughly one-carbon-atom diameter. [34], a charged fermion in curved surface subject to external electric field is analyzed in the stationary optical metric conformal to the BTZ black hole. We study physical properties of a charged fermion confined on the surface of wormhole in the presence of the external magnetic field along the axis direction of the wormhole. 3, the Dirac equation in curved spacetime is used to analyze the (1+2)-dimensional stationary state of the charged fermion in the wormhole.
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