Torsion effects on a relativistic position-dependent mass system

Abstract

We analyse a relativistic scalar particle with a position-dependent mass in a spacetime with a space-like dislocation by showing that relativistic bound states solutions can be achieved. Further, we consider the presence of the Coulomb potential and analyse the relativistic position-dependent mass system subject to the Coulomb potential in the spacetime with a space-like dislocation. We also show that a new set of relativistic bound states solutions can be obtained, where there also exists the influence of torsion of the relativistic energy levels. Finally, we investigate an analogue of the Aharonov-Bohm effect for bound states in this position-dependent mass in a spacetime with a space-like dislocation.

Linear confinement of a scalar particle in a Gödel-type spacetime

“…[39], we see that the vorticity of the spacetime and the deficit of the angle modify the relativistic energy level of the ground state. In the SomRaychaudhuri spacetime with a cosmic string, the ground state of the linear confinement of a relativistic scalar particle has two allowed energies as shown in Eq.…”

“…Note that the problem which is investigated in this work is very different from that investigated in Refs. [37][38][39]. Here, we investigate the relativistic spinless quantum particle in a rotating spacetime in the presence of a topological defect.…”

Harmonic oscillator in an elastic medium with a spiral dislocation

“…By comparing with the Aharonov-Bohm-type effect for bound states discussed in Refs. [16,23,26] (where the topology of the screw dislocation also modifies the angular momentum), we have that the effects of the topology of the spiral dislocation on the energy levels (11) yield no change in the angular momentum quantum number. In this sense, there is no Aharonov-Bohm-type effect for bound states [7,21,33].…”

“…In particular, torsion effects related to the presence of topological defects are in the interests of studies of semiconductors [17][18][19][20]. Moreover, spacetimes with space-like disclinations and with space-like dislocations [4] have also been investigated as backgrounds of relativistic quantum systems [21][22][23][24][25][26][27]. On the hand, studies of an edge dislocation through differential geometry and its influence on quantum systems have not been widely explored.…”

On the Majorana fermion subject to a linear confinement

“…It is worth pointing out that, by modifying the mass term of either Dirac or Klein-Gordon equations, we build a relativistic analogue of the position-dependent mass systems [29][30][31]. Effects associated with the linear confinement have also been investigated in different relativistic quantum system [32][33][34][35][36][37][38][39][40] and in the presence of topological defects in the spacetime [41][42][43]. Hence, we search for relativistic bound state solutions to a Majorana fermion subject to a linear scalar potential.…”