K. Bakke

Landau quantization for a neutral particle in the presence of topological defects

In this paper we study the Landau levels in the nonrelativistic dynamics of a neutral particle which possesses a permanent magnetic dipole moment interacting with an external electric field in the curved space-time background with the presence or absence of a torsion field. The eigenfunction and eigenvalues of the Hamiltonian are obtained. We show that the presence of the topological defect breaks the infinite degeneracy of the Landau levels arising in this system. We also apply a duality transformation to discuss this same quantization for a dynamics of a neutral particle with a permanent electric dipole moment.

Geometric phase for a neutral particle in the presence of a topological defect

In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved space-time. The nonrelativistic quantum dynamics are investigated using the Foldy-Wouthuysen expansion. The gravitational Aharonov-Casher and He-McKellar-Wilkens effects are investigated for a series of electric and magnetic field configurations.

Relativistic Landau-Aharonov-Casher quantization based on the Lorentz symmetry violation background

Based on the discussions about the Aharonov-Casher effect in the Lorentz symmetry violation background, we show that the analogue of the relativistic Landau quantization in the Aharonov-Casher setup can be achieved in the Lorentz-symmetry violation background.

Noninertial effects on the Dirac oscillator in a topological defect spacetime

In this paper, we study the influence of noninertial effects on the Dirac oscillator in the cosmic string spacetime background. We discuss the behaviour of the oscillator frequency in a noninertial system that allows us to obtain relativistic bound state solutions. We also discuss the influence of the topology of the cosmic string spacetime on the relativistic energy levels, and obtain the Dirac spinors for positive-energy solutions. Furthermore, by taking the nonrelativistic limit of the energy levels, we compare the nonrelativistic energy levels to the confinement of a spin-half particle to quantum dot described by the Tan-Inkson model for a quantum dot (W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11, 1635 (1996)), and a hard-wall confining potential (E. Tsitsishvili et al., Phys. Rev. B 70, 115316 (2004)).

On the interaction of the Dirac oscillator with the Aharonov-Casher system in topological defect backgrounds

Abstract In this paper, we study the influence of the Aharonov–Casher effect [Y. Aharonov, A. Casher, Phys. Rev. Lett. 53 (1984) 319] on the Dirac oscillator in three different scenarios of general relativity: the Minkowski spacetime, the cosmic string spacetime and the cosmic dislocation spacetime. In this way, we solve the Dirac equation and obtain the energy levels for bound states and the Dirac spinors for positive-energy solutions. We show that the relativistic energy levels depend on the Aharonov–Casher geometric phase. We also discuss the influence of curvature and torsion on the relativistic energy levels and the Dirac spinors due to the topology of the cosmic string and cosmic dislocation spacetimes.

Threading dislocation densities in semiconductor crystals: A geometric approach

Abstract In this Letter, we introduce a geometric model to explain the origin of the observed shallow levels in semiconductors threaded by a dislocation density. We show that a uniform distribution of screw dislocations acts as an effective uniform magnetic field which yields bound states for a spin-half quantum particle, even in the presence of a repulsive Coulomb-like potential. This introduces energy levels within the band gap, increasing the carrier concentration in the region threaded by the dislocation density and adding additional recombination paths other than the near band-edge recombination.

Relativistic Landau quantization for a neutral particle

In this contribution we study the Landau levels arising within the relativistic quantum dynamics of a neutral particle which possesses a permanent magnetic dipole moment interacting with an external electric field. We consider the Aharonov-Casher coupling of magnetic dipole to the electric field to investigate an an analog of Landau quantization in this system and solve the Dirac equation for two different field configurations. The eigenfunctions and eigenvalues of Hamiltonian in both cases are obtained.

On the Klein–Gordon oscillator subject to a Coulomb-type potential

By introducing the scalar potential as modification in the mass term of the Klein-Gordon equation, the influence of a Coulomb-type potential on the Klein-Gordon oscillator is investigated. Relativistic bound states solutions are achieved to both attractive and repulsive Coulomb-type potentials and the arising of a quantum effect characterized by the dependence of angular frequency of the Klein-Gordon oscillator on the quantum numbers of the system is shown.

THE ANALOGUE OF THE AHARONOV–BOHM EFFECT FOR BOUND STATES FOR NEUTRAL PARTICLES

We study the analogue of the Aharonov–Bohm effect for bound states for a neutral particle with a permanent magnetic dipole moment interacting with an external field. We consider a neutral particle confined to moving between two coaxial cylinders and show the dependence of the energy levels on the Aharonov-Casher quantum flux. Moreover, we show that the same flux dependence of the bound states can be found when the neutral particle is confined to a one-dimensional quantum ring and a quantum dot, and we also calculate the persistent currents in each case.

Bound states for a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field

Abstract We discuss the arising of bound states solutions of the Schrodinger equation due to the presence of a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field. Furthermore, we study the influence of the Coulomb-type potential on the harmonic oscillator by showing a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system, whose meaning is that not all values of the angular frequency are allowed.