Revisiting the controversy over the time-dependent Aharonov-Bohm effect
The time-dependent Aharonov-Bohm (AB) effect considers the situation in which the magnetic flux inside the solenoid changes time-dependently. Different from the standard AB-effect, the problem is unexpectedly subtle and not easy to solve without any doubt, which is the reason why it is still in a st...
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Format | Journal Article |
Language | English |
Published |
25.06.2024
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Abstract | The time-dependent Aharonov-Bohm (AB) effect considers the situation in which
the magnetic flux inside the solenoid changes time-dependently. Different from
the standard AB-effect, the problem is unexpectedly subtle and not easy to
solve without any doubt, which is the reason why it is still in a state of
unsettlement even theoretically. The difficulty originates from the fact that
its theoretical analysis requires line-integral along a path in the
4-dimensional Minkowski space. The central controversy concerns the success or
failure of the claim by Singleton and collaborators, which states that the
time-dependent part of the AB-phase shift due to the magnetic vector potential
is precisely cancelled by the effect of induced electric field generated by the
time-variation of the magnetic flux. In this paper, we try to demonstrate that
their cancellation argument would not be justified by going back to the basic
quantum mechanical analysis of the charged particle motion under the presence
of external electromagnetic potential. At the end, we conclude that the failure
of the cancellation argument is due to unjustified application of the
4-dimensional Stokes theorem to the problem of time-dependent AB-effect. |
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AbstractList | The time-dependent Aharonov-Bohm (AB) effect considers the situation in which
the magnetic flux inside the solenoid changes time-dependently. Different from
the standard AB-effect, the problem is unexpectedly subtle and not easy to
solve without any doubt, which is the reason why it is still in a state of
unsettlement even theoretically. The difficulty originates from the fact that
its theoretical analysis requires line-integral along a path in the
4-dimensional Minkowski space. The central controversy concerns the success or
failure of the claim by Singleton and collaborators, which states that the
time-dependent part of the AB-phase shift due to the magnetic vector potential
is precisely cancelled by the effect of induced electric field generated by the
time-variation of the magnetic flux. In this paper, we try to demonstrate that
their cancellation argument would not be justified by going back to the basic
quantum mechanical analysis of the charged particle motion under the presence
of external electromagnetic potential. At the end, we conclude that the failure
of the cancellation argument is due to unjustified application of the
4-dimensional Stokes theorem to the problem of time-dependent AB-effect. |
Author | Wakamatsu, Masashi |
Author_xml | – sequence: 1 givenname: Masashi surname: Wakamatsu fullname: Wakamatsu, Masashi |
BackLink | https://doi.org/10.48550/arXiv.2406.18046$$DView paper in arXiv |
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Snippet | The time-dependent Aharonov-Bohm (AB) effect considers the situation in which
the magnetic flux inside the solenoid changes time-dependently. Different from... |
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SubjectTerms | Physics - High Energy Physics - Phenomenology Physics - Nuclear Theory Physics - Physics Education Physics - Quantum Physics |
Title | Revisiting the controversy over the time-dependent Aharonov-Bohm effect |
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