Geometric phase for a neutral particle in the presence of a topological defect

Abstract

In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic fields in this curved background. The nonrelativistic quantum dynamics are investigated using the Foldy-Wouthuysen expansion. The gravitational Aharonov-Casher and He-Mckellar-Wilkens effects are investigated for a series of electric and magnetic fields configurations.

Influences of a topological defect on the spin Hall effect

“…But in our case its value is zero, and then has no influence. The term α · Γ is directly from the spin connection of the minimal-like interaction, and behaves like an hidden momentum then be able to generate a geometric phase [32]. The term c α · Ω · π is induced by the geometry of the cosmic string space-time, and is determined by g µν (x).…”

“…Here ∇ µ = ∂ µ +Γ µ is the covariant derivative determined by the geometry of background space-time, and ω µab (x) is the one connection ω ab (x) = ω µab (x)dx µ , its solutions can be obtained by using the Maurer-Cartan structure equation [32],…”

“…And more recently, the relativistic and non relativistic quantum dynamics of a neutral particle with permanent magnetic and electric dipole moments were studied in the curved space time [30]. The topological Aharonov-Bohm and Aharonov-Casher effects have also been studied in the presence of a topological defect [31,32]. In this paper, we focus on the influence of topological defects on spin currents and their deformation on the spin Hall conductivity.…”

Landau quantization for a neutral particle in the presence of topological defects

“…The relativistic dynamics of the neutral particle in this curved spacetime was studied in [48]. In the same paper, the non-relativistic behavior of the neutral particle in curved spacetime was obtained through the application of the Foldy-Wouthuysen approximation [43] to the Dirac equation.…”

“…The relativistic and non-relativistic quantum dynamics of a neutral particle with permanent magnetic and electric dipole moments which interacts with externals fields was studied in flat spacetime in [37], in the curved spacetime in [26,48] and in the presence of a torsion field in [49]. In this paper, we construct an analog of Landau quantization for a neutral particle with permanent magnetic dipole moment which interacts with an external electric field in a cosmic string and cosmic dislocation spacetime.…”