The canonical Aharonov–Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov–Bohm phase acquired by a charged particle moving in time-dependent potentials. In particular, we focus on the case of a charged particle moving in the time-varying field of a plane electromagnetic wave. We work out the Aharonov–Bohm phase using both the potential (i.e. $\oint A_\mu \mathrm{d}x ^\mu$ ) and the field (i.e. $\frac{1}{2}\int F_{\mu \nu } \mathrm{d}\sigma ^{\mu \nu }$ ) forms of the Aharonov–Bohm phase. We give conditions in terms of the parameters of the system (frequency of the electromagnetic wave, the size of the space–time loop, amplitude of the electromagnetic wave) under which the time-varying Aharonov–Bohm effect could be observed.The canonical Aharonov–Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov–Bohm phase acquired by a charged particle moving in time-dependent potentials. In particular, we focus on the case of a charged particle moving in the time-varying field of a plane electromagnetic wave. We work out the Aharonov–Bohm phase using both the potential (i.e. $$\oint A_\mu \mathrm{d}x ^\mu $$ ) and the field (i.e. $$\frac{1}{2}\int F_{\mu \nu } \mathrm{d}\sigma ^{\mu \nu }$$ ) forms of the Aharonov–Bohm phase. We give conditions in terms of the parameters of the system (frequency of the electromagnetic wave, the size of the space–time loop, amplitude of the electromagnetic wave) under which the time-varying Aharonov–Bohm effect could be observed.

arXiv:1509.01646The European Physical Journal CSep 1, 201510 citations

The time-dependent aharonov-bohm effect

James B. Macdougall

Jan 1, 20160 citations

Time-dependent Aharonov-Bohm effect for electromagnetic and gravitational scalar potentials

R. Y. Chiao, Nader A. Inan, Michael Scheibner +3 more

Abstract In this article, we review a new approach to the scalar Aharonov-Bohm effect for both the electromagnetic and gravitational interaction. For both interactions a quantum system is placed in a time-dependent electromagnetic or gravitational potential, but with no force (spatial derivative of the potential) acting on the quantum system. Nevertheless, we show that the energy levels of the quantum system develop side bands which can be detected as the signature of this version of the scalar Aharonov-Bohm effect. We briefly look at the specific experimental setups required to detect the energy side bands.Abstract In this article, we review a new approach to the scalar Aharonov-Bohm effect for both the electromagnetic and gravitational interaction. For both interactions a quantum system is placed in a time-dependent electromagnetic or gravitational potential, but with no force (spatial derivative of the potential) acting on the quantum system. Nevertheless, we show that the energy levels of the quantum system develop side bands which can be detected as the signature of this version of the scalar Aharonov-Bohm effect. We briefly look at the specific experimental setups required to detect the energy side bands.

Journal of Physics Conference SeriesNov 1, 20241 citation

Aharonov–Bohm Effect under Self-duality Condition of Electromagnetic Field

H. Torres‐Silva, A. Domínguez-Pacheco, J. Lopez-Bonilla +1 more

We discuss the situation of Aharonov–Bohm effect under self-duality condition of electromagnetic field, where there is no exact cancellation of the AB(t) phase shift because this phase shift is complex. This means that the time-dependent AB effect, magnetic AB phase shift is not canceled out by a phase shift coming from the Lorentz force with E=−∂tA. Our approach can be compared with the results obtained by other authors which have shown that AB(t) effect vanishes for Abelian electromagnetic plane waves.We discuss the situation of Aharonov–Bohm effect under self-duality condition of electromagnetic field, where there is no exact cancellation of the AB(t) phase shift because this phase shift is complex. This means that the time-dependent AB effect, magnetic AB phase shift is not canceled out by a phase shift coming from the Lorentz force with E=−∂tA. Our approach can be compared with the results obtained by other authors which have shown that AB(t) effect vanishes for Abelian electromagnetic plane waves.

Prespacetime journalMay 12, 20160 citations

The time-dependent, relativistic Aharonov-Bohm effect

Zachary Kertzman, A. Petridis

Bulletin of the American Physical SocietyOct 11, 20070 citations

\oint A_\mu \mathrm{d}x ^\mu

) and the field (i.e.

\frac{1}{2}\int F_{\mu \nu } \mathrm{d}\sigma ^{\mu \nu }

) forms of the Aharonov–Bohm phase. We give conditions in terms of the parameters of the system (frequency of the electromagnetic wave, the size of the space–time loop, amplitude of the electromagnetic wave) under which the time-varying Aharonov–Bohm effect could be observed.