On the Influence of Curvature on the Landau–he–mckellar–wilkens Quantization Induced by Noninertial Effects

Abstract

We consider a neutral particle with permanent electric dipole moment interacting with a field configuration induced by the noninertial effects of the Fermi-Walker reference frame in the presence of a disclination and discuss the influence of curvature on the Landau-He -McKellar-Wilkens quantization.

A comment on the analogous confinement of a neutral particle to a quantum dot via noninertial effects

“…In the following, we discuss the nonrelativistic limit of the Dirac equation and the analogous confinement of the neutral particle to a quantum dot with a hard-wall confining potential [33][34][35][36][37]. Recently, the Fermi-Walker reference frame has been used in several distinct studies such as holonomies in curved spacetime background [18], relativistic Einstein-Podolsky-Rosen correlations [19], geometric quantum phases for neutral particles [17], Landau quantization for a neutral particle [24][25][26], and two-dimensional quantum dots [30,31]. We consider a system with cylindrical symmetry, where we can write the line element in the form:…”

“…In the Fermi-Walker reference frame we can observe noninertial effects from the action of external forces without any effects from arbitrary rotations of the local spatial axis. Following the above definition of the Fermi-Walker reference frame, we can write the tetrads and its inverse in the form [17,[24][25][26]:…”

“…By solving the MaurerCartan structure equations, the non-null components of the connecetions 1-form are ω 1 2 ( ) = −ω 2 1 ( ) = −1 and ω 1 2 ( ) = −ω 2 1 ( ) = −ω. Now, let us discuss how the noninertial effects of the Fermi-Walker reference frame can induce a field configuration which allow us to obtain either a Landau system for a neutral particle with a permanent electric dipole moment [24][25][26] or confine the neutral particle to a quantum dot. First of all, we consider a uniform electric field along the axis in the rest frame of the observer, thus, we write this electric field in the form: E 3 = 3 E = E 0 .…”

“…Thus, substituting this solution into the Dirac equation (6), we obtain two coupled equation of φ and χ. After some calculations to decouple the equation for φ and χ, the Schrödinger-Pauli equation for a neutral particle with a permanent electric dipole moment interacting with external electric and mag-netic fields in the Fermi-Walker reference frame is [24][25][26] …”

“…In Ref. [24][25][26], it has been shown that the Landau-HeMcKellar-Wilkens quantization [27][28][29] can be obtained without assuming the existence of magnetic charges. Recently, bound states for a neutral particle with permanent magnetic dipole moment analogous to a quantum dot have been obtained via the noninertial effects of the FermiWalker reference frame [30][31][32].…”