Relativistic Landau quantization in the spiral dislocation spacetime

Abstract

We analyse the interaction of a relativistic electron with a uniform magnetic field in the spiral dislocation spacetime. We show that analytical solutions to the Dirac equation can be obtained, where the spectrum of energy corresponds to the relativistic Landau levels. We also analyse the influence of the spiral dislocation on the relativistic Landau levels by showing that there exists an analogue of the Aharonov–Bohm effect for bound states.

Topological Effects of a Spiral Dislocation on Quantum Revivals

“…Recently, we have studied the harmonic oscillator under the influence of the spiral dislocation (1) by assuming that β 2 is very small [21]. This assumption has allowed us to analyse the asymptotic behaviour of the radial wave function when r → 0, as we can consider x → 0 [23]. In the present work, by contrast, we do not assume that β is very small.…”

“…Let us introduce the spiral dislocation that corresponds to the distortion of a circle into a spiral [21][22][23]45]. Based on the Katanaev-Volovich approach [34], the spiral dislocation is described by the line element:…”

“…However, there is no cross-revival time for a particle confined to a twodimensional quantum ring in the presence of the spiral dislocation. It is worth observing that the revival time related to the radial quantum number (21) differs from the revival time related to the angular momentum number (23). Furthermore, we can assume that the relation between τ (1) and τ (2) is satisfied, i.e., τ (1) τ (2) = ā b , where ā and b are relatively prime integers.…”

Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials

“…In addition, cosmic string space–time has also been studied in the context of the Kaluza–Klein theory in the literature (see [17,18] and related references therein). Some other investigations of the topological defect are Dirac fermions with Kratzer-like potential under Lorentz symmetry violation in a space–time with screw dislocation [19], a static composite structure under magnetic field in the spiral dislocation space–time [20], in a cosmic string space–time with distortion of a radial line into a spiral on the scalar field [21], free fermions in the presence of spiral dislocation in a space–time with distortion of a radial line into spiral [22], interactions of an electron with non-uniform electric field under cut-off point induced by spiral dislocation [23], spiral dislocation on the confinement of a point charge under the rotating frame of reference [24], and interactions of an electron with magnetic field in a space–time with spiral dislocation [25].…”