Topological and noninertial effects in an Aharonov–Bohm ring

Abstract

In this paper, we study the influence of topological and noninertial effects on a Dirac particle confined in an Aharonov-Bohm (AB) ring. Next, we explicitly determine the Dirac spinor and the energy spectrum for the relativistic bound states. We observe that this spectrum depends on the quantum number n, magnetic flux Φ of the ring, angular velocity ω associated to the noninertial effects of a rotating frame, and on the deficit angle η associated to the topological effects of a cosmic string. We verified that this spectrum is a periodic function and grows in values as a function of n, Φ, ω, and η. In the nonrelativistic limit, we obtain the equation of motion for the particle, where now the topological effects are generated by a conic space. However, unlike relativistic case, the spectrum of this equation depends linearly on the velocity ω and decreases in values as a function of ω. Comparing our results with other works, we note that our problem generalizes some particular cases of the literature. For instance, in the absence of the topological and noninertial effects (η = 1 and ω = 0) we recover the usual spectrum of a particle confined in an AB ring (Φ = 0) or in an 1D quantum ring (Φ = 0).

Topological Effects of a Spiral Dislocation on Quantum Revivals

“…Based on nonrelativistic wave equations, several studies have shown the influence of linear topological defects on the electronic properties of solids [41][42][43][44][45][46][47][48]. Linear topological defects have also been studied in quantum rings [49][50][51][52], for an electron subject to the deformed Kratzer potential [53] and subject to a uniform magnetic field [54][55][56][57]. The most promising perspective in the studies of linear topological defects is the appearance of Aharonov-Bohm-type effects [58][59][60][61].…”

Relativistic Quantum Motion of an Electron in Spinning Cosmic String Spacetime in the Presence of Uniform Magnetic Field and Aharonov-Bohm Potential

“…As a final comment, we would like to emphasize that the model studied in this article generalizes others found in the literature, such as those of Refs. [68,72] for the case including a superposition of external magnetic fields and the investigation of isolated solutions of the Dirac equation. Furthermore, we present a detailed discussion on the energy levels of the particle which, in general, is not found in the literature.…”

“…This way, it is also an attractive question examining how the electromagnetic interactions affect the particle quantum motion of a rotating system in the presence of a topological defect. Reference [68], for instance, is a recent work dealing with both topological and noninertial effects in the presence of an Aharonov-Bohm potential. Reference [69] addresses the problem of a spinless relativistic particle subjected to a uniform magnetic field in the spinning cosmic string spacetime.…”

Effects of rotation and Coulomb type potential on the spin-1/2 Aharonov-Bohm problem

“…Currently, there still exists a debate on the origin, interpretations and implications of the AB effect [16][17][18][19]. There are also relevant works in the literature on the AB effect applied to other physical systems, for example, problems involving spin and pseudo-spin symmetries [20][21][22][23][24][25][26][27][28], topological defects [29][30][31][32][33][34][35], thermodynamic aspects [36][37][38][39][40][41][42][43], κ-deformed algebra [44,45], Lorentz symmetry violation [46][47][48][49] and Duffin-Kemmer-Petiau (DKP) formalism [50][51][52][53]. Another topic of central importance in this context refers to the description of the AB effect by taking into account the electron spin degree of freedom [54].…”