Time-dependent Aharonov-Bohm effect on the noncommutative space

Abstract

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. \draftnote{The net correction is proportional to the product of the magnetic fluxes through the fundamental area represented by the noncommutative parameter $\theta$, 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 $\Phi /N$ (N is the number of fringes shifted). This nontrivial relation can also provide a way to test the spatial noncommutativity. For $B\Phi /N\sim 1$, our estimation on the experimental sensitivity shows that it can reach the $10GeV$ 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.

12 pages, 1 figure; v2, accepted version by PLB

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• Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics
• Probing the noncommutative effects of phase space in the time-dependent Aharonov-Bohm effect
• Quantum speed limit for a relativistic electron in the noncommutative phase space
• Probing Noncommutativities of Phase Space by Using Persistent Charged Current and Its Asymmetry
• Covariant version of Pauli Hamiltonian, spin-induced non commutativity, Thomas precession and precession of spin
• Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space
• Influences of the coordinate dependent noncommutative space on charged and spin currents
• Chiral Spin Noncommutative Space and Anomalous Dipole Moments
• Noncommutative effects on the fluid dynamics and modifications of the Freidmann equation
• Zitterbewegung in Noncommutative Geometry