arXiv subjects

K. Bakke

Publications and source records attributed to K. Bakke.

At least 19 recordsLinked to original sources

arXiv2025

Induced electric dipole moment coupling in Dirac equation

We introduce a nonminimal coupling into the Dirac equation as a model of describing the interaction of a Dirac neutral particle with an induced electric dipole moment with magnetic and electric fields. Then, we obtain a relativistic geometric quantum phase from the interaction of the induced electric dipole moment with electric and magnetic fields. Further, we include the permanent magnetic dipole moment of the Dirac neutral particle besides the induced electric dipole moment and obtain the relativistic geometric quantum phase.

quant-ph↗

arXiv2025

Revisiting the missing He-McKellar-Wilkens geometric quantum phase

We discuss the missing He-McKellar-Wilkens geometric quantum phase in Landau levels for a neutral particle with a permanent electric dipole moment in the presence of an infinity wall. We also discuss the influence of the missing He-McKellar-Wilkens geometric quantum phase on the energy levels of a neutral particle confined to a one-dimensional quantum ring. Further, we explore this influence of the missing He-McKellar-Wilkens geometric quantum phase on the energy levels by calculating the persistent spin currents.

quant-ph↗

arXiv2025

Missing Aharonov-Casher geometric quantum phase

From the interaction of the permanent magnetic dipole moment of a neutral particle with an electric field inside a long non-conducting cylindrical shell of inner radius $r_{a}$ and outer radius $r_{b}$, we show that a geometric quantum phase stems from the missing electric charge per unit length. Thus, we discuss the possibility of existing Aharonov-Bohm-type effects with regard to this geometric quantum phase. Further, we discuss the persistent spin currents.

quant-ph↗

arXiv2024

Modified attractive inverse-square potential in the induced electric dipole system

We examine the spatial distribution of electric charges within an extended, non-conductive cylinder featuring an inner radius denoted as $r_{0}$. Our investigation unveils the emergence of a distinct modified attractive-inverse square potential, arising from the intricate interplay between the electric field and the induced electric dipole moment of a neutral particle. This modified potential notably departs from the conventional inverse-square potential, showcasing an additional term proportional to $r^{-1}$. As a result, we present compelling evidence for the realization of a discrete energy spectrum within this intricate system.

quant-ph↗

arXiv2024

On the attractive inverse-square potential in the induced electric dipole system under the influence of the harmonic oscillator

We obtain the analytical solutions to the Schr\"odinger equation for the attractive inverse-square potential in an induced electric dipole moment system under the influence of the harmonic oscillator. We show that bound states can exist when the electric field configuration brings a cut-off point that imposes a forbidden region for the neutral particle. Then, by dealing with $s$-waves, we obtain the energy eigenvalues in the strong electric field regime and for small values of the angular frequency of the harmonic oscillator. Further, we extend our discussion about the energy eigenvalues beyond the $s$-waves.

quant-ph↗

arXiv2022

On the missing magnetic flux and topological effects of a screw dislocation on a charged particle in an inhomogeneous magnetic field

We study the interaction of an electron/hole with inhomogeneous magnetic field in the presence of a screw dislocation. We consider the internal structure of the defect, i.e., we consider the core that gives rise to a finite size to the defect. In addition, we assume that this core determines a forbidden region for the electron/hole. Then, we solve the Schrödinger equation and show that an Aharonov-Bohm-type effect arises from the influence of the topological defect and the missing magnetic flux on the eigenvalues of energy.

quant-ph↗

arXiv2020

Aharonov-Bohm effect for bound states in the cosmic string spacetime in the context of rainbow gravity

We explore a scenario of the general relativity determined by the framework of the rainbow gravity with the purpose of searching for analogues of the Aharonov-Bohm effect. By focusing on the confinement of the Dirac field and the scalar field to a hard-wall confining potential in a modified background of the cosmic string spacetime, we examine the effects of the rainbow gravity and the topology of the cosmic string spacetime. Then, we compare each spectrum of energy with the cases where the rainbow gravity is absent.

hep-th↗

arXiv2019

Non-relativistic quantum effects on the harmonic oscillator in a spacetime with a distortion of a vertical line into a vertical spiral

Non-relativistic quantum effects of the topology of the spacetime with the distortion of a vertical line into a vertical spiral on the harmonic oscillator are investigated. By searching for analytical solutions to the Schrödinger equation in this topological defect background, it is shown that the topology of the spacetime modifies the spectrum of energy of the harmonic oscillator. Besides, it is shown that there exists an Aharonov-Bohm-type effect for bound states.

physics.gen-ph↗

arXiv2019

Effects of rotation in the spacetime with a distortion of a vertical line into a vertical spiral

It is investigated the effects of rotation on the scalar field in the spacetime with the distortion of a vertical line into a vertical spiral. By analysing the upper limit of the radial coordinate that stems from the effects of rotation and the topology of the defect, it is considered this upper limit of the radial coordinate as a boundary condition analogous to a hard-wall confining potential. Then, it is obtained a relativistic spectrum of energy in a particular case. In addition, it is analysed a relativistic analogue of the Aharonov-Bohm effect for bound states.

physics.gen-ph↗

arXiv2019

On an electron in an elastic medium with a spiral dislocation

Topological effects of a spiral dislocation on an electron are investigated when it is confined to a hard-wall confining potential. Besides, it is analysed the influence of the topology of the spiral dislocation on the interaction of the electron with a non-uniform radial electric field and a uniform axial magnetic field. It is shown that a discrete spectrum of energy can be obtained in all these cases. Moreover, it is shown that there is one case where an analogue of the Aharonov-Bohm effect for bound states is yielded by the topology of the spiral dislocation.

cond-mat.mes-hall↗

arXiv2019

Topological and rotating effects on the Dirac field in the spiral dislocation spacetime

By considering a spacetime with a spiral dislocation, we analyse the behaviour of the Dirac field subject to a hard-wall confining potential. In search of relativistic bound states solutions, we discuss the influence of the topology of the spiral dislocation spacetime on the energy levels. Further, we analyse the effects of rotation on the Dirac field in the spiral dislocation spacetime. We show that both rotation and the topology of the spacetime impose a restriction on the values of the radial coordinate. Thus, we analyse the effects of rotation and the topology of the spiral dislocation spacetime on the Dirac field subject to a hard-wall confining potential by searching for relativistic bound states solutions.

quant-ph↗

arXiv2019

Aharonov-Bohm-type effect in the background of a distortion of a vertical line into a vertical spiral

It is analysed Aharonov-Bohm-type effects when a spinless quantum particle is in an elastic medium with the distortion of a vertical line into a vertical spiral. By confining the spinless particle to a cylindrical box, the analogue of the Aharonov-Bohm effect for bound states is observed due to influence of the topological defect on the allowed energies of the system. It corresponds to the shift in the angular momentum quantum number yielded by the effects of the topology of the distortion of a vertical line into a vertical spiral. In addition, it is analysed the effects of rotation. It is shown that the Aharonov-Bohm effect for bound states exists. Besides, there is an analogue of the coupling between the angular momentum and angular velocity of the rotating frame.

quant-ph↗

arXiv2019

A doubly anharmonic oscillator in an induced electric dipole system

The behaviour of the interaction of the induced electric dipole moment of an atom with a uniform magnetic field and a non-uniform electric field are investigated in a rotating reference frame. An interesting aspect of this interaction is that it gives rise to an analogue of a spinless particle subject to the doubly anharmonic oscillator. Then, it is shown that analytical solutions to the Schrödinger equation can be obtained. Another point raised is that the quantum effects on the induced electric dipole moment can be observed if the uniform magnetic field possesses a discrete set of values.

quant-ph↗

arXiv2019

A semiclassical treatment of the interaction of non-uniform electric fields with the electric quadrupole moment of a neutral particle

By applying the WKB (Wentzel, Kramers, Brillouin) approximation, we analyse the interaction of the electric quadrupole moment of a neutral particle with radial electric fields produced by a non-uniform electric charge densities. Then, we show particular cases of this interaction where a discrete spectrum of energy can be achieved for the s-waves of the neutral particle.

quant-ph↗

arXiv2018

Scalar Casimir effect in a high-dimensional cosmic dispiration spacetime

In this paper we present a complete and detailed analysis of the calculation of both the Wightman function and the vacuum expectation value of the energy-momentum tensor that arise from quantum vacuum fluctuations of massive and massless scalar fields in the cosmic dispiration spacetime, which is formed by the combination of two topological defects: a cosmic string and a screw dislocation. This spacetime is obtained in the framework of the Einstein-Cartan theory of gravity and is considered to be a chiral space-like cosmic string. For completeness we perform the calculation in a high-dimensional spacetime, with flat extra dimensions. We found closed expressions for the the energy-momentum tensor and, in particular, in (3+1)-dimensions, we compare our results with existing previous ones in the literature for the massless scalar field case.

hep-th↗

arXiv2018

Dirac ocillator in the cosmic string spacetime in the context of gravity's rainbow

In this paper we consider the Dirac oscillator in the context of Doubly General Relativity or Gravity's Rainbow. In order to obtain the energy levels of the Dirac oscillator, we solve the Dirac equation in the cosmic string spacetime modified by gravity's rainbow scenarios described by two rainbow functions. We then obtain that, as a consequence of the modification of the cosmic string line element by the two rainbow functions, the energy levels of the Dirac oscillator are appreciable altered. The results are plotted and compared with the standard case, without gravity's rainbow effects.

gr-qc↗

arXiv2018

Rotating effects on the scalar field in the cosmic string spacetime, in the spacetime with space-like dislocation and in the spacetime with a spiral dislocation

In the interface between general relativity and relativistic quantum mechanics, we analyse rotating effects on the scalar field subject to a hard-wall confining potential. We consider three different scenarios of general relativity given by the cosmic string spacetime, the spacetime with space-like dislocation and the spacetime with a spiral dislocation. Then, by searching for a discrete spectrum of energy, we analyse analogues effects of the Aharonov-Bohm effect for bound states and the Sagnac effect.

gr-qc↗

arXiv2018

Harmonic oscillator in an elastic medium with a spiral dislocation

We investigate the behaviour of a two-dimensional harmonic oscillator in an elastic medium that possesses a spiral dislocation (an edge dislocation). We show that the Schrödinger equation for harmonic oscillator in the presence of a spiral dislocation can be solved analytically. Further, we discuss the effects of this topological defect on the confinement to a hard-wall confining potential. In both cases, we analyse if the effects of the topology of the spiral dislocation gives rise to an Aharonov-Bohm-type effect for bound states.

quant-ph↗