Aharonov-Bohm Phase for an Electric Dipole on a Noncommutative Space

Abstract

We study the non-relativistic behavior of a particle with electric dipole moment and interacting with external electromagnetic fields on a noncommutative space (NCS). For a special configuration of the field, the phase of an electric dipole is derived as an application of the Aharonov-Bohm effect to a system composed of two charges. We find that the quantum phase for an electric dipole obtains some corrections, and these corrections depend on the noncommutative parameter explicitly.

Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

“…The expression of the obtained phase includes an additional term dependent on the NC space parameter, θ (measured in units of (length) 2 ). The limit on θ found in the AB effect is of the order of √ θ 10 6 GeV −1 which corresponds to a relatively large scale of 1 Å [8]. This same approach was extended to the Aharonov-Casher (AC) [10] effect by Li and Wang [11], and Mirza and Zarei [12], in this effect two coherent beams of neutral particles encircle an infinite charged wire.…”

“…Recently there has been a growing interest in studying quantum mechanics in noncommutative (NC) space [1][2][3] [4][5] [6]. Because quantum nature experiments are measured with high precision, these are feasible scenarios for setting limits on the experimental manifestation of NC space.…”

Time-dependent Aharonov–Casher effect on noncommutative space

“…It was shown that Lorentz symmetry was violated if the tenser θ μν is nondynamical [20]. Electromagnetic interactions of dipole moments can receive additional contributions [21][22][23][24][25][26][27][28], and degenerate levels of hydrogen energy spectrum can be removed [29][30][31]. Apart from the dynamical effects, topological properties of the ordinary electromagnetic theory can also be distorted, for instance, the Aharonov-Bohm (AB) effect [32] and the Aharonov-Casher (AC) effect [33] on noncommutative spacetime [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] as well as in the spacetime of topological defects [49][50][51], can receive non-trivial corrections.…”

Investigation of the Aharonov-Bohm and Aharonov-Casher topological phases for quantum entangled states

“…In recent years, studies on AB-type effects have focused on investigating the time dependence of the effect. Singleton et al discussed two covariant generalizations of the AB effect with time-dependent flux, noting that the AB phase shift is canceled by the phase shift of the external electric field associated with the Lorentz force [11], Bright et al explored the time-dependent (TD) AB effect for non-Abelian gauge fields revealing cancellations between phase shifts from non-Abelian electromagnetic fields [12], Ababekri et al examined the non-relativistic behavior of particles with electric dipoles on noncommutative space uncovering quantum phase corrections [13], Singleton et al developed a covariant expression for the AC phase, investigating its interaction with electromagnetic fields [14], Jing et al re-examined the AB effect in the background of a time-dependent vector potential, highlighting alterations in interference patterns [15], Ma et al explored noncommutative corrections to the TD-AB effect by revealing three types of corrections and proposing dimensionless quantities for parameter extraction based on measured phase shifts [16], Choudhury et al discovered a frequency-dependent AB phase shift [17], Jing et al revisited the TD-AB effects in noncommutative space-time, finding no noncommutative corrections to the AB effects for both cases up to the first order of the noncommutative parameter [18], Wang et al investigated the TD-HMW effect in noncommutative space by confirming gauge symmetry, and time-dependent AC effect and its corrections due to spatial noncommutativity on noncommutative space [19; 20], Saldanha proposed an electrodynamic AB scheme challenging the topological nature of the phase [21], and Wakamatsu et al analyzed the AB effect's interaction energy and its gauge invariance [22].…”