Electric Aharonov-Bohm Effect on a Noncommutative Space

Kai Ma, Jian-Hua Wang

K. Li, S. Dulat

E. Comay

G. Eskin

Kai Ma, Jian-Hua Wang, Huan-Xiong Yang

We study the time-dependent Aharonov–Bohm effect on the noncommutative space. Because there is no net Aharonov–Bohm phase shift in the time-dependent case on the commutative space, therefore, a tiny deviation from zero indicates new physics . Based on the Seiberg–Witten map we obtain the gauge invariant and Lorentz covariant Aharonov–Bohm phase shift in general case on noncommutative space. We find there are two kinds of contribution: momentum-dependent and momentum-independent corrections. For the momentum-dependent correction, there is a cancellation between the magnetic and electric phase shifts, just like the case on the commutative space. However, there is a non-trivial contribution in the momentum-independent correction. This is true for both the time-independent and time-dependent Aharonov–Bohm effects on the noncommutative space. However, for the time-dependent Aharonov–Bohm effect, there is no overwhelming background which exists in the time-independent Aharonov–Bohm effect on both commutative and noncommutative space. Therefore, the time-dependent Aharonov–Bohm can be sensitive to the spatial noncommutativity. The net correction is proportional to the product of the magnetic fluxes through the fundamental area represented by the noncommutative parameter θ , and through the surface enclosed by the trajectory of charged particle. More interestingly, there is an anti-collinear relation between the logarithms of the magnetic field B and the averaged flux Φ / N ( N is the number of fringes shifted). This nontrivial relation can also provide a way to test the spatial noncommutativity. For B Φ / N ∼ 1 , our estimation on the experimental sensitivity shows that it can reach the 10 GeV scale. This sensitivity can be enhanced by using stronger magnetic field strength , larger magnetic flux, as well as higher experimental precision on the phase shift.

Mamutjan Ababekri, Abduwali Anwar, Mamatabdulla Hekim +1 more

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, we derived the phase of an electric dipole as an application of the AB effect to a system composed of two charges. We find that the quantum phase for electric dipole obtains some correction, and this correction depend on the noncommutative parameter explicitly.