Knut Bakke

We investigate the effects of the Lorentz symmetry violation on the Wigner rotation in cosmic string space–time through the Fermi–Walker transport of spinors. We establish two possible scenarios of the Lorentz symmetry violation in cosmic string space–time. Then, we analyze the effects of the topology of the cosmic string space–time, the accelerated motion of the particle, the position of the observers and the Lorentz symmetry violation background on the Wigner rotation angle. In addition, we analyze these effects on the relativistic EPR (Einstein–Podolsky–Rosen) correlations and Bell’s inequality.

We introduce a non-Hermitian operator which has exponentially decreasing energy levels and study the Aharonov–Bohm effect for bound states. Further, we include the two-dimensional harmonic oscillator in this non-Hermitian quantum system and obtain real energy levels with exponentially decrease. We also show that the Aharonov–Bohm effect for bound states exists in this second case. In both cases, we go further by showing that non-null persistent currents at zero temperature and non-null revival times exist.

With nonuniform crossed electric and magnetic fields inside a long nonconducting cylinder, we show that a non-null nonclassical moment of inertia (at zero temperature) and revival time can be obtained for s -wave from the interaction of these fields with the induced electric dipole moment of a neutral particle combined with rotation.

With a point charge in an elastic medium with a uniform distribution of parallel screw dislocations in a rotating reference frame, we show that the infinity degeneracy of the energy levels obtained in Ref. [27] is broken by the effects of rotation and their dependence on the magnetic flux. We go further by showing that a non-null moment of inertia at zero temperature exists at the quantum level, and how the magnetic flux influences it. We also extend our discussion to the appearance of persistent currents at zero temperature in this elastic medium.

By dealing with an elastic medium with a disclination, we search for the influence of the disclination topology on a geometric quantum phase yielded by the interaction of a nonuniform magnetic field with the permanent electric dipole moment of a neutral particle. This magnetic field is produced by a nonuniform electric current density. Further, we explore the non-Abelian nature of the geometric quantum phase in search of quantum holonomies for this neutral particle system and discuss a possible application to the geometric quantum computation.

We study the arising of Landau levels in the region outside the magnetic quantum dot under the influence of the spiral dislocation topology. We show that Aharonov–Bohm-type effects stem from the missing magnetic flux and the spiral dislocation topology. Further, we discuss the influence of the missing magnetic flux and the spiral dislocation topology on the magnetization, magnetic susceptibility and persistent currents at zero temperature in the region outside the magnetic quantum dot.

We study the influence of the Aharonov-Bohm quantum phase on a quantum system described by a non-Hermitian Hamiltonian. We show that a non-Hermitian Hamiltonian has real energy eigenvalues which are influenced by the Aharonov-Bohm quantum phase. In addition, we show that persistent currents can arise. Finally, we calculate the revival times in this two-dimensional system and show that they are influenced by Aharonov-Bohm quantum phase.

In this paper, we study the interaction of an electron with a linear radial electric field inside a nonconducting elastic medium with a spiral dislocation in a rotating reference frame. We first show that the spin–orbit coupling yielded by the radial electric field does not produce the well-known Rashba coupling, but a different contribution. Then, from the analytical solutions to the Schrödinger equation, we analyze the effects of rotation, the spin–orbit coupling and the spiral dislocation topology on the interaction of an electron with the linear radial electric field.

By considering the cosmic string space–time, we study the interaction of a spinless electrically charged particle with the uniform magnetic field in the region outside the magnetic quantum dot. We show that the missing magnetic flux is influenced by the topology of the cosmic string. In addition, we obtain the Landau levels by assuming that an impenetrable potential wall is located at the radius [ ] of the cylinder that defines the magnetic quantum dot. Then, we show that an Aharonov–Bohm-type effect for bound states can be achieved from the cosmic string space–time topology and the missing magnetic flux. Further, we extend our discussion to the magnetization and persistent currents at zero temperature.