Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space

Abstract

We examine the bound state and scattering problem of a spin-one-half particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit. The crucial problem of the δ-function singularity coming from the Zeeman spin interaction with the magnetic flux tube is solved through the self-adjoint extension method. Using two different approaches already known in the literature, both based on the self-adjoint extension method, we obtain the self-adjoint extension parameter to the bound state and scattering scenarios in terms of the physics of the problem. It is shown that such a parameter is the same for both situations. The method is general and is suitable for any quantum system with a singular Hamiltonian that has bound and scattering states.

Revtex4, 5 pages, published version

References in corpus (17)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Anomalous Aharonov-Bohm conductance oscillations from topological insulator surface states
• Aharonov-Bohm interferences from local deformations in graphene
• Aharonov-Bohm Effect with $\delta$--type Interaction
• Geometric Phase for Neutral Particle in the Presence of a Topological Defect
• Lensing effects in a nematic liquid crystal with topological defects
• Continuum effects for the mean-field and pairing properties of weakly bound nuclei
• Path integral treatment of two- and three-dimensional delta-function potentials and application to spin-1/2 Aharonov-Bohm problem
• On the quantum dynamics of a point particle in conical space
• Effects of Anomalous Magnetic Moment in the Quantum Motion of Neutral Particle in Magnetic and Electric Fields Produced by a Linear Source in a Conical Spacetime
• Effects of Nongauge Potentials on the Spin-1/2 Aharonov-Bohm Problem
• Self-adjoint Extension Approach to the spin-1/2 Aharonov-Bohm-Coulomb Problem
• Green functions for generalized point interactions in 1D: A scattering approach
• A pragmatic approach to the problem of the self-adjoint extension of Hamilton operators with the Aharonov-Bohm potential
• Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian
• Propagator for spinless and spin-1/2 Aharonov-Bohm-Coulomb systems

Cited by in corpus (42)

• Thermodynamic properties of neutral particle in presence of Topological defects in Magnetic Cosmic String Background
• Noninertial effects on the quantum dynamics of scalar bosons
• Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background
• Quantum dynamics of scalar bosons in a cosmic string background
• Bound states for a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field
• Threading dislocation densities in semiconductor crystals: a geometric approach
• Vacuum currents induced by a magnetic flux around a cosmic string with finite core
• Scattering and bound states of Dirac Equation in presence of cosmic string for Hulthén potential
• Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem
• On the Dirac oscillator in a spinning cosmic string spacetime in external magnetic fields: Investigation of energy spectrum and connection with the condensed matter physics
• Analogue Aharonov-Bohm effect in a Lorentz-violating background
• Nonrelativistic quantum dynamics on a cone with and without a constraining potential
• Remarks on the Aharonov-Casher dynamics in a CPT-odd Lorentz-violating background
• Bound states of massive fermions in the Aharonov--Bohm-like fields
• On the spin-1/2 Aharonov-Bohm problem in conical space: bound states, scattering and helicity nonconservation
• Semiclassical gravitational effects on the gravitational lensing in the spacetime of topological defects
• Quantum motion of a point particle in the presence of the Aharonov--Bohm potential in curved space
• The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle
• Noncommutative analogue Aharonov-Bohm effect and superresonance
• On Aharonov-Casher bound states
• Landau levels, self-adjoint extensions and Hall conductivity on a cone
• Topological and noninertial effects in an Aharonov-Bohm ring
• Study of electronic properties, Magnetization and persistent currents in a mesoscopic ring by controlled curvature
• Modifications of electron states, magnetization and persistent current in a quantum dot by controlled curvature
• One-dimensional scattering of fermions on $\delta$-impurities
• Electric quadrupole moment of a neutral non-relativistic particle in the presence of screw dislocation
• Relativistic quantum dynamics of neutral particle in external electric fields: An approach on effects of spin
• Induced fermionic charge and current densities in two-dimensional rings
• Influence of spatially varying pseudo-magnetic field on a 2D electron gas in graphene
• On planar quantum dynamics of a magnetic dipole moment in the presence of electric and magnetic fields
• Quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field with scalar and vector couplings
• Study on the effects of anisotropic effective mass on electronic properties, magnetization and persistent current in semiconductor quantum ring with conical geometry
• Finite temperature fermion condensate, charge and current densities in a (2+1)-dimensional conical space
• Vacuum polarization of charged massless fermions in Coulomb and Aharonov--Bohm fields
• Effect of vacuum polarization of charged massive fermions in an Aharonov--Bohm field
• Relativistic quantum dynamics of vector bosons in an Aharonov-Bohm potential
• Self-adjoint extension approach for singular Hamiltonians in (2+1) dimensions
• Effects of rotation and Coulomb type potential on the spin-1/2 Aharonov-Bohm problem
• Quasi-stationary states and fermion pair creation from a vacuum in supercritical Coulomb field
• Quantum motion of a spinless particle in curved space: A viewpoint of scattering theory
• Quantum states of a neutral massive fermion with an anomalous magnetic moment in an external electric field
• Effects of curvature on the electronic states of a two-dimensional mesoscopic ring