Searcharxiv⌕ Search

arXiv subjects

K. Bakke

Publications and source records attributed to K. Bakke.

At least 37 records · Page 2Linked to original sources
arXiv2018

Linear confinement of a scalar particle in a Gödel-type spacetime

Based on the studies of confinement of quarks, we introduce a linear scalar potential into the relativistic quantum dynamics of a scalar particle. Then, we analyse the linear confinement of a relativistic scalar particle in a Gödel-type spacetime in the presence of a topological defect. We consider a Gödel-type spacetime associated with null curvature, i.e., the Som-Raychaudhuri spacetime, which is characterized by the presence of vorticity in the spacetime. Then, we search for analytical solutions to the Klein-Gordon equation and analyse the influence of the topology of the cosmic string and the vorticity on the relativistic energy levels.

gr-qc↗
arXiv2017

Coulomb-type interaction under Lorentz symmetry breaking effects

Based on models of confinement of quarks, we analyse a relativistic scalar particle subject to a scalar potential proportional to the inverse of the radial distance and under the effects of the violation of the Lorentz symmetry. We show that the effects of the Lorentz symmetry breaking can induced a harmonic-type potential. Then, we solve the Klein-Gordon equation analytically and discuss the influence of the background of the violation of the Lorentz symmetry on the relativistic energy levels.

hep-ph↗
arXiv2017

On the Majorana fermion subject to a linear confinement

We analyse the linear confinement of a Majorana fermion in $\left(1+1\right)$-dimensions. We show that the Dirac equation can be solved analytically. Besides, we show that the spectrum of energy is discrete, however, the energy levels are not equally spaced.

quant-ph↗
arXiv2017

Noninertial effects on nonrelativistic topological quantum scattering

We investigate noninertial effects on the scattering problem of a nonrelativistic particle in the cosmic string spacetime. By considering the nonrelativistic limit of the Dirac equation we are able to show, in the regime of small rotational frequencies, that the phase shift has two contribution: one related to the noninertial reference frame, and the other, due to the cosmic string conical topology. We also show that both the incident wave and the scattering amplitude are altered as a consequence of the noninertial reference frame and depend on the rotational frequency.

quant-ph↗
arXiv2017

Aharonov-Bohm effect for bound states in relativistic scalar particle systems in a spacetime with a space-like dislocation

We investigate the analogue effect of the Aharonov-Bohm effect for bound states in two relativistic quantum systems in a spacetime with a space-like dislocation. We assume that the topological defect has an internal magnetic flux. Then, we analyse the interaction of a charged particle with a uniform magnetic field in this topological defect spacetime, and thus, we extend this analysis to the confinement to a hard-wall potential and a linear scalar potential. Later, the interaction of the Klein-Gordon oscillator with a uniform magnetic field is analysed. We first focus on the effects of torsion that stem from the spacetime with a space-like dislocation and the geometric quantum phase. Then, we analyse the effects of torsion and the geometric quantum phase under the presence of a hard-wall potential and a linear scalar potential.

quant-ph↗
arXiv2017

On an atom with a magnetic quadrupole moment in a rotating frame

The quantum description of an atom with a magnetic quadrupole moment in the presence of a uniform effective magnetic field is analysed. The atom is also subject to rotation and a scalar potential proportional to the inverse of the radial distance. It is shown that the spectrum of energy is modified, in contrast to the Landau-type levels, and there is a restriction on the possible values of the cyclotron frequency which stems from the influence of the rotation and scalar potential proportional to the inverse of the radial distance.

quant-ph↗
arXiv2017

Quantum effects on an atom with a magnetic quadrupole moment in a region with a time-dependent magnetic field

The quantum description of an atom with a magnetic quadrupole moment in the presence of a time-dependent magnetic field is analysed. It is shown that the time-dependent magnetic field induces an electric field that interacts with the magnetic quadrupole moment of the atom and gives rise to a Landau-type quantization. It is also shown that a time-independent Schrödinger equation can be obtained, i.e., without existing the interaction between the magnetic quadrupole moment of the atom and the time-dependent magnetic field, therefore, the Schrödinger equation can be solved exactly. It is also analysed this system subject to scalar potentials.

quant-ph↗
arXiv2017

A relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry

We consider a background of the violation of the Lorentz symmetry determined by the tensor $\left( K_{F}\right)_{μναβ}$ which governs the Lorentz symmetry violation out of the Standard Model Extension, where this background gives rise to a Coulomb-type potential, and then, we analyse its effects on a relativistic quantum oscillator. Furthermore, we analyse the behaviour of the relativistic quantum oscillator under the influence of a linear scalar potential and this background of the Lorentz symmetry violation. We show in both cases that analytical solutions to the Klein-Gordon equation can be achieved.

quant-ph↗
arXiv2017

Fermions in Gödel-type background space-times with torsion and the Landau quantization

In this paper, we analyze Dirac fermions in Gödel-type background space-times with torsion. We also consider the Gödel-type spacetimes embedded in a topological defect background. We show that relativistic bound states solutions to the Dirac equation can be obtained by dealing with three cases of the Gödel-type solutions with torsion, where a cosmic string passes through these three cases of the space-time. We obtain the relativistic energy levels for all cases of the Gödel-type solutions with torsion with a cosmic string, where we show that there exists an analogy with the Landau levels for Dirac particles. We also show that the presence of torsion in the space-time yields new contributions to the relativistic spectrum of energies and that the presence of the topological defect modifies the degeneracy of the relativistic energy levels.

hep-th↗
arXiv2016

Torsion effects on a relativistic position-dependent mass system

We analyse a relativistic scalar particle with a position-dependent mass in a spacetime with a space-like dislocation by showing that relativistic bound states solutions can be achieved. Further, we consider the presence of the Coulomb potential and analyse the relativistic position-dependent mass system subject to the Coulomb potential in the spacetime with a space-like dislocation. We also show that a new set of relativistic bound states solutions can be obtained, where there also exists the influence of torsion of the relativistic energy levels. Finally, we investigate an analogue of the Aharonov-Bohm effect for bound states in this position-dependent mass in a spacetime with a space-like dislocation.

quant-ph↗
arXiv2016

On a neutral particle with a magnetic quadrupole moment in a uniform effective magnetic field

Quantum effects on a Landau-type system associated with a moving atom with a magnetic quadrupole moment subject to confining potentials are analysed. It is shown that the spectrum of energy of the Landau-type system can be modified, where the degeneracy of the energy levels can be broken. In three particular cases, it is shown that the analogue of the cyclotron frequency is modified, and the possible values of this angular frequency of the system are determined by the quantum numbers associated with the radial modes and the angular momentum and by the parameters associated with confining potentials in order that bound states solutions can be achieved.

quant-ph↗
arXiv2016

Rotating effects on the Landau quantization for an atom with a magnetic quadrupole moment

Based on the single particle approximation [V. F. Dmitriev {\it et al}, Phys. Rev. C {\bf50}, 2358 (1994), C.-C. Chen, Phys. Rev. A {\bf51}, 2611 (1995)], the Landau quantization associated with an atom with a magnetic quadrupole moment is introduced, and then, rotating effects on this analogue of the Landau quantization is investigated. It is shown that rotating effects can modify the cyclotron frequency and breaks the degeneracy of the analogue of the Landau levels.

quant-ph↗
arXiv2016

On an atom with a magnetic quadrupole moment subject to harmonic and linear confining potentials

The quantum dynamics of an atom with a magnetic quadrupole moment that interacts with an external field subject to a harmonic and a linear confining potentials is investigated. It is shown that the interaction between the magnetic quadrupole moment and an electric field gives rise to an analogue of the Coulomb potential and, by confining this atom to a harmonic and a linear confining potentials, a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system is obtained. In particular, it is shown that the possible values of the angular frequency associated with the ground state of the system are determined by a third-degree algebraic equation.

quant-ph↗
arXiv2015

On a relativistic scalar particle subject to the Klein-Gordon oscillator, the Coulomb potential and a linear scalar potential

The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed: a dependence of the angular frequency of the Klein-Gordon oscillator on the quantum numbers of the system. The meaning of this behaviour of the angular frequency is that only some specific values of the angular frequency of the Klein-Gordon oscillator are permitted in order to obtain bound state solutions. As an example, we obtain both the angular frequency and the energy level associated with the ground state of the relativistic system. Further, we analyse the behaviour of an electrically charged particle subject to the Klein-Gordon oscillator, the Coulomb potential and a linear scalar potential.

quant-ph↗
arXiv2015

Lorentz symmetry breaking effects on relativistic EPR correlations

Lorentz symmetry breaking effects on relativistic EPR (Einstein-Podolsky-Rosen) correlations are discussed. From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the Lorentz symmetry violation and write an effective metric for the Minkowski spacetime. Then, we obtain the Wigner rotation angle via the Fermi-Walker transport of spinors and consider the WKB ((Wentzel-Kramers-Brillouin) approximation in order to study the influence of Lorentz symmetry breaking effects on the relativistic EPR correlations.

hep-th↗
arXiv2015

An angular frequency dependence on the Aharonov-Casher geometric phase

A quantum effect characterized by a dependence of the angular frequency associated with the confinement of a neutral particle to a quantum ring on the quantum numbers of the system and the Aharonov-Casher geometric phase is discussed. Then, it is shown that persistent spin currents can arise in a two-dimensional quantum ring in the presence of a Coulomb-type potential. A particular contribution to the persistent spin currents arises from the dependence of the angular frequency on the geometric quantum phase.

quant-ph↗
arXiv2015

A Landau-type quantization from a Lorentz symmetry violation background with crossed electric and magnetic fields

We investigate the arising of an analogue of the Landau quantization from a background of the violation of the Lorentz symmetry established by a time-like 4-vector and a field configuration of crossed electric and magnetic field. We also analyse the effects on this Landau-type system subject to a hard-wall confining potential by showing a particular case where a discrete spectrum of energy can be obtained. Further, we analyse the effects of a linear confining potential on the Landau-type system. We show that a quantum effect characterized by the dependence of the cyclotron frequency on the quantum numbers of the system can arise in this analogue of the Landau system. As an example, we calculate the cyclotron frequency associated with ground state of the system.

hep-th↗