Edilberto O. Silva

Effects of quantum deformation on the spin-1/2 Aharonov–Bohm problem

Abstract In this Letter we study the Aharonov–Bohm problem for a spin-1/2 particle in the quantum deformed framework generated by the κ -Poincare–Hopf algebra. We consider the nonrelativistic limit of the κ -deformed Dirac equation and use the spin-dependent term to impose an upper bound on the magnitude of the deformation parameter e . By using the self-adjoint extension approach, we examine the scattering and bound state scenarios. After obtaining the scattering phase shift and the S -matrix, the bound states energies are obtained by analyzing the pole structure of the latter. Using a recently developed general regularization prescription [Phys. Rev. D. 85 (2012) 041701(R)], the self-adjoint extension parameter is determined in terms of the physics of the problem. For last, we analyze the problem of helicity conservation.

Remarks on the Aharonov-Casher dynamics in a CPT-odd Lorentz-violating background

The Aharonov-Casher problem in the presence of a Lorentz-violating background nonminimally coupled to a spinor and a gauge field is examined. Using an approach based on the self-adjoint extension method, an expression for the bound-state energies is obtained in terms of the physics of the problem by determining the self-adjoint extension parameter.

Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background

In this work the dynamics of a 2D Dirac oscillator in the spacetime of a magnetic cosmic string is considered. It is shown that earlier approaches to this problem have neglected a

On the spin- 1/2 Aharonov-Bohm problem in conical space: Bound states, scattering and helicity nonconservation

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2DEG on a cylindrical shell with a screw dislocation

δ function contribution to the full Hamiltonian, which comes from the Zeeman interaction. The inclusion of spin effects leads to results which confirm a modified dynamics. Based on the self-adjoint extension method, we determined the most relevant physical quantities, such as energy spectrum, wave functions and the self-adjoint extension parameter by applying boundary conditions allowed by the system.

Landau quantization, Aharonov–Bohm effect and two-dimensional pseudoharmonic quantum dot around a screw dislocation

In this work bound states for the Aharonov–Casher problem are considered. According to Hagen’s work on the exact equivalence between spin-1/2 Aharonov–Bohm and Aharonov–Casher effects, is known that the ∇⋅E term cannot be neglected in the Hamiltonian if the spin of particle is considered. This term leads to the existence of a singular potential at the origin. By modeling the problem by boundary conditions at the origin which arises by the self-adjoint extension of the Hamiltonian, we derive for the first time an expression for the bound state energy of the Aharonov–Casher problem. As an application, we consider the Aharonov–Casher plus a two-dimensional harmonic oscillator. We derive the expression for the harmonic oscillator energies and compare it with the expression obtained in the case without singularity. At the end, an approach for determination of the self-adjoint extension parameter is given. In our approach, the parameter is obtained essentially in terms of physics of the problem.

On the κ-Dirac oscillator revisited

In this work the bound state and scattering problems for a spin-1/2 particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a \delta-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and

On Aharonov–Casher scattering in a CPT-odd Lorentz-violating background

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