Aharonov–Bohm phase for an electromagnetic wave background

Bright, Max; Singleton, Douglas; Yoshida, Atsushi

doi:10.1140/epjc/s10052-015-3670-8

Cited by 10 publications

(19 citation statements)

References 22 publications

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“…We see that this result agrees with the spacetime line integral of the 4-vector potential from (16) or (17). Thus we find that, for this case, the time-dependent 4D version of Stokes' theorem is satisfied.…”

Section: The Infinite Time-dependent Solenoidsupporting

confidence: 84%

“…(3) does not have a well known right hand rule as is the case for purely spatial contours and areas. The directionality that we have chosen above for the spacetime area is taken so that the area integral of the fields in (18) agrees with the results of the contour integrals of the two vector potentials given in (16) and (17) for the closed contour given in Fig. (2) (i.e.…”

Section: Appendix IIImentioning

confidence: 77%

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Time dependent electromagnetic fields and 4-dimensional Stokes' theorem

Andosca

Singleton

2016

American Journal of Physics

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Stokes' theorem is central to many aspects of physics -- electromagnetism, the Aharonov-Bohm effect, and Wilson loops to name a few. However, the pedagogical examples and research work almost exclusively focus on situations where the fields are time-independent so that one need only deal with purely spatial line integrals ({\it e.g.} $\oint {\bf A} \cdot d{\bf x}$) and purely spatial area integrals ({\it e.g.} $\int (\nabla \times {\bf A}) \cdot d{\bf a} = \int {\bf B} \cdot d{\bf a}$). Here we address this gap by giving some explicit examples of how Stokes' theorem plays out with time-dependent fields in a full 4-dimensional spacetime context. We also discuss some unusual features of Stokes' theorem with time-dependent fields related to gauge transformations and non-simply connected topology.Comment: 25 pages ReVTeX, 5 eps figures, 3 appendices. To be published American Journal of Physic

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Section: The Infinite Time-dependent Solenoidsupporting

confidence: 84%

Section: Appendix IIImentioning

confidence: 77%

Time dependent electromagnetic fields and 4-dimensional Stokes' theorem

Andosca

Singleton

2016

American Journal of Physics

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“…We would also comment on our calculation and result in relation to two other relevant investigations of ABE II. Bright et al [18] have investigated time dependent ABE II wherein the time dependence of the fields comes from an electromagnetic wave background. The cancellation of the electric and magnetic fringe shifts was shown to be approximate.…”

Section: Discussionmentioning

confidence: 99%

Direct calculation of time varying Aharonov-Bohm effect

Choudhury

Mahajan

2019

Physics Letters A

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The Aharonov-Bohm effect (ABE) for steady magnetic fields is a well known phenomenon. However, if the current in the infinite solenoid that creates the magnetic field is time-dependent, that is in the presence of both magnetic and electric fields, there is no agreement whether the effect would be present. In this note, we try to investigate time varying ABE by a direct calculation in a set-up with a weak time dependent magnetic field. We find that the electric field arising out of the time-varying magnetic field in the path of the electrons does not enter the action integral but only changes the path of the electron from the source to the slits and then on to the detector. We find a frequency dependent AB phase shift. At low frequencies the result smoothly approaches the one for a constant field as the frequency tends towards zero. On the other hand, for high frequencies such that the AB-phase induced in the path of the wave packet oscillates rapidly, the net effect will be very small which is borne out by our results.

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“…(3) are taken into account. It has been shown that as long as the charging rate of the magnetic field is considerably larger than the typical scale of the particle traveling between the source and screen, there is no net phase shift in the time-dependent Aharonove-Bohm effects [31,32,33,34,35,36]. Therefore the time-dependent AB effect can be employed to investigate tiny derivation from zero in the phase shift which is induced by unknown new physics at high energy scale.…”

Section: Introductionmentioning

confidence: 99%

Probing the noncommutative effects of phase space in the time-dependent Aharonov–Bohm effect

Ma¹,

Wang²,

Yang³

2017

Annals of Physics

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We study the noncommutative corrections on the time-dependent Aharonov-Bohm effect when both the coordinate-coordinate and momentum-momentum noncommutativities are considered. This study is motivated by the recent observation that there is no net phase shift in the time-dependent AB effect on the ordinary space, and therefore tiny derivation from zero can indicate new physics. The vanishing of the timedependent AB phase shift on the ordinary space is preserved by the gauge and Lorentz symmetries. However, on the noncomutative phase space, while the ordinary gauge symmetry can be kept by the Seiberg-Witten map, but the Lorentz symmetry is broken. Therefore nontrivial noncommutative corrections are expected.We find there are three kinds of noncommutative corrections in general: 1) ξ-dependent correction which comes from the noncommutativity among momentum operators; 2) momentum-dependent correction which is rooted in the nonlocal interactions in the noncommutative extended model; 3) momentum-independent correction which emerges become of the gauge invariant condition on the nonlocal interactions in the noncommutative model. We proposed two dimensionless quantities, which are based on the distributions of the measured phase shift with respect to the external magnetic field and to the cross section enclosed by the particle trajectory, to extract the noncommutative parameters. We find that stronger (weaker) magnetic field strength can give better bounds on the coordinate-coordinate (momentum-momentum) noncommutative parameter, and large parameter space region can be explored by the time-dependent AB effect.

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Aharonov–Bohm phase for an electromagnetic wave background

Cited by 10 publications

References 22 publications

Time dependent electromagnetic fields and 4-dimensional Stokes' theorem

Time dependent electromagnetic fields and 4-dimensional Stokes' theorem

Direct calculation of time varying Aharonov-Bohm effect

Probing the noncommutative effects of phase space in the time-dependent Aharonov–Bohm effect

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