arXiv subjects

K. Bakke

Publications and source records attributed to K. Bakke.

At least 55 records · Page 3Linked to original sources

arXiv2015

On a relativistic scalar particle subject to a Coulomb-type potential given by Lorentz symmetry breaking effects

The behaviour of a relativistic scalar particle in a possible scenario that arises from the violation of the Lorentz symmetry is investigated. The background of the Lorentz symmetry violation is defined by a tensor field that governs the Lorentz symmetry violation out of the Standard Model Extension. Thereby, we show that a Coulomb-type potential can be induced by Lorentz symmetry breaking effects and bound states solutions to the Klein-Gordon equation can be obtained. Further, we discuss the effects of this Coulomb-type potential on the confinement of the relativistic scalar particle to a linear confining potential by showing that bound states solutions to the Klein-Gordon equation can also be achieved, and obtain a quantum effect characterized by the dependence of a parameter of the linear confining potential on the quantum numbers $\left\{n,l\right\}$ of the system.

hep-th↗

arXiv2015

Wigner rotation via Fermi-Walker transport and relativistic EPR correlations in the Schwarzschild spacetime

The Wigner rotation angle for a particle in a circular motion in the Schwarzschild spacetime is obtained via the Fermi-Walker transport of spinors. Then, by applying the WKB approximation, a possible application of the Fermi-Walker transport of spinors in relativistic EPR correlations is discussed, where it is shown that the spins of the correlated particle undergo a precession in an analogous way to that obtained by Terashima and Ueda [H. Terashima and M. Ueda, Phys. Rev. A {\bf69}, 032113 (2004)] via the application of successive infinitesimal Lorentz transformations. Moreover, from the WKB approach, it is also shown that the degree of violation of the Bell inequality depends on the Wigner rotation angle obtained via the Fermi-Walker transport. Finally, the relativistic effects from the geometry of the spacetime and the accelerated motion of the correlated particles is discussed in the nonrelativistic limit.

quant-ph↗

arXiv2015

Relativistic scalar particle subject to a confining potential and Lorentz symmetry breaking effects in the cosmic string spacetime

The behaviour of a relativistic scalar particle subject to a scalar potential under the effects of the violation of the Lorentz symmetry in the cosmic string spacetime is discussed. It is considered two possible scenarios of the Lorentz symmetry breaking in the CPT-even gauge sector of the Standard Model Extension defined by a tensor $\left(K_{F}\right)_{μναβ}$. Then, by introducing a scalar potential as a modification of the mass term of the Klein-Gordon equation, it is shown that the Klein-Gordon equation in the cosmic string spacetime is modified by the effects of the Lorentz symmetry violation backgrounds and bound state solution to the Klein-Gordon equation can be obtained.

hep-th↗

arXiv2015

He-McKellar-Wilkens-type effect from the Lorentz symmetry breaking effects

From the effects of the Lorentz symmetry violation in the CPT-even gauge sector of Standard Model Extension, we establish a possible scenario where an analogue of the He-McKellar-Wilkens effect can stem from. Besides, we build quantum holonomies associated with the analogue of the He-McKellar-Wilkens effect and discuss a possible analogy with the holonomic quantum computation [P. Zanardi and M. Rasetti, Phys. Lett. A {\bf264}, 94 (1999)]. Finally, we investigate the dependence of the energy levels on the He-McKellar-Wilkens geometric phase induced by Lorentz symmetry breaking effects when the particle is confined to a hard-wall confining potential.

hep-th↗

arXiv2014

On the influence of a Rashba-type coupling induced by Lorentz-violating effects on a Landau system for a neutral particle

We study a possible scenario of the Lorentz symmetry violation background that allows us to build an analogue of the Landau system for a nonrelativistic Dirac neutral particle interacting with a field configuration of crossed electric and magnetic fields. We also discuss the arising of analogues of the Rashba coupling, the Zeeman term and the Darwin term from the Lorentz symmetry breaking effects, and the influence of these terms on the analogue of the Landau system confined to a two-dimensional quantum ring. Finally, we show that this analogy with the Landau system confined to a two-dimensional quantum ring allows us to establish an upper bound for the Lorentz symmetry breaking parameters.

hep-th↗

arXiv2014

Relativistic geometric quantum phases from the Lorentz symmetry violation effects in the CPT-even gauge sector of Standard Model Extension

We discuss the appearance of relativistic geometric quantum phases for a Dirac neutral particle based on possible scenarios of the Lorentz symmetry violation background in the CPT-even gauge sector of Standard Model Extension. Relativistic analogues of the Anandan quantum phase [J. Anandan, Phys. Lett. A 138, 347 (1989)] are obtained based on the the parity-even and parity-odd sectors of the tensor $\left(K_{F}\right)_{μναβ}$.

hep-th↗

arXiv2014

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.

quant-ph↗

arXiv2014

Geometric quantum phases from Lorentz symmetry breaking effects in the cosmic string spacetime

By starting from the modified Maxwell theory coupled to gravity, the arising of geometric quantum phases in the relativistic and nonrelativistic quantum dynamics of a Dirac neutral particle from the effects of the violation of the Lorentz symmetry in the cosmic string spacetime is investigated. It is shown that the Dirac equation can be written in terms of an effective metric and a relativistic geometric phase stems from the topology of the cosmic string spacetime and the Lorentz symmetry breaking effects. Further, the nonrelativistic limit of the Dirac equation is discussed and it is shown that both Lorentz symmetry breaking effects and the topology of the defect yields a phase shift in the wave function of the nonrelativistic spin-1/2 particle.

hep-th↗

arXiv2014

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

We discuss the arising of bound states solutions of the Schrödinger 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.

quant-ph↗

arXiv2014

Torsion and noninertial effects on a nonrelativistic Dirac particle

We investigate torsion and noninertial effects on a spin-$1/2$ quantum particle in the nonrelativistic limit of the Dirac equation. We consider the cosmic dislocation spacetime as a background and show that a rotating system of reference can be used out to distances which depend on the parameter related to the torsion of the defect. Therefore, we analyse torsion effects on the spectrum of energy of a nonrelativistic Dirac particle confined to a hard-wall potential in a Fermi-Walker reference frame.

quant-ph↗

arXiv2014

Noninertial effects on the ground state energy of a massive scalar field in the cosmic string spacetime

We investigate the influence of noninertial effects on the ground state energy of a massive scalar field in the cosmic string spacetime. We generalize the results obtained by Khusnutdinov and Bordag [N. R. Khusnutdinov and M. Bordag, Phys. Rev. D 59, 064017 (1999)] to a noninertial reference frame and show, by contrast, that a non-vanishing contribution to the ground state energy stems from the noninertial effects. Moreover, we show that there is no influence of the curvature of the spacetime on this non-vanishing contribution to the ground state energy of a massive scalar field.

hep-th↗

arXiv2013

Rotating effects on the Dirac oscillator in the cosmic string spacetime

In this contribution, we study the Dirac oscillator under the influence of noninertial effects of a rotating frame in the cosmic string spacetime. We show that both noninertial effects and the topology of the cosmic string spacetime restrict the physical region of the spacetime where the quantum particle can be placed, and discuss two different cases of bound states solutions of the Dirac equation by analysing the behaviour of the Dirac oscillator frequency.

quant-ph↗

arXiv2013

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

In this paper, we study the influence of the Aharonov-Casher effect [Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984).] 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.

quant-ph↗

arXiv2013

Persistent spin currents in an elastic Landau system

We consider a neutral particle with permanent magnetic dipole moment in an elastic medium with the presence of a uniform distribution of screw dislocations interacting with a radial electric field. We show that the uniform distribution of dislocations plays the role of an effective uniform magnetic field, and obtain a spectrum of energy which depends on the Aharonov-Casher geometric phase [Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984)]. Moreover, from the dependence of energy levels on the Aharonov-Casher geometric phase, we calculate the persistent spin currents in this elastic Landau system.

quant-ph↗

arXiv2013

Relativistic Landau-He-McKellar-Wilkens quantization and relativistic bound states solutions for a Coulomb-like potential induced by the Lorentz symmetry breaking effects

In this work, we discuss the relativistic Landau-He-McKellar-Wilkens quantization and relativistic bound states solutions for a Dirac neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present new possible scenarios of studying Lorentz symmetry breaking effects by fixing the space-like vector field background in special configurations. It is worth mentioning that we use the criterion for studying the violation of Lorentz symmetry is that the gauge symmetry should be preserved.

hep-th↗

arXiv2013

Quantum Holonomies based on the Lorentz-violating tensor background

We study geometric quantum phases corresponding to analogues of the Anandan quantum phase [J. Anandan, Phys. Lett. A {\bf138}, 347 (1989)] based on a possible scenario of the Lorentz symmetry violation background in a tensor background. We also show that quantum holonomies associated with the analogue of the Anandan quantum phase can be determined, and discuss a way of performing one-qubit quantum gates by analogy with the holonomic quantum computation [P. Zanardi and M. Rasetti, Phys. Lett. A {\bf264}, 94 (1999)].

hep-th↗

arXiv2012

Kaluza-Klein description of geometric phases in graphene

In this paper, we use the Kaluza-Klein approach to describe topological defects in a graphene layer. Using this approach, we propose a geometric model allowing to discuss the quantum flux in $K$-spin subspace. Within this model, the graphene layer with a topological defect is described by a four-dimensional metric, where the deformation produced by the topological defect is introduced via the three-dimensional part of metric tensor, while an Abelian gauge field is introduced via an extra dimension. We use this new geometric model to discuss the arising of topological quantum phases in a graphene layer with a topological defect.

cond-mat.mes-hall↗

arXiv2012

Threading dislocation densities in semiconductor crystals: a geometric approach

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.

quant-ph↗