A possible interplay between electron beams and magnetic fluxes in the Aharonov–Bohm effect

doi:10.1007/s11467-015-0470-4

Frontiers of Physics

2015, Vol. 10

Issue (3): 100305 https://doi.org/10.1007/s11467-015-0470-4

RESEARCH ARTICLE

本期目录

A possible interplay between electron beams and magnetic fluxes in the Aharonov–Bohm effect

Wang Rui-Feng（王瑞峰）(

)

Department of Physics, Beijing Jiaotong University, Beijing 100044, China

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Abstract：

Most studies on the magnetic Aharonov–Bohm (A–B) effect focus on the action exerted by the magnetic flux on the electron beam, but neglect the back-action exerted by the electron beam on the magnetic flux. This paper focuses on the latter, which is the electromotive force ΔU across the solenoid induced by the time-dependent magnetic field of the electron beam. Based on the backaction analysis, we observe that the magnetic A–B effect arises owing to the interaction energy between the magnetic field of the electron beam and the magnetic field of the solenoid. We also demonstrate that the interpretation attributing the magnetic A–B effect to the vector potential violates the uncertainty principle.

Key words： Aharonov–Bohm effect uncertainty principle superconductivity superconducting quantum interference device (SQUID)

收稿日期: 2014-11-05 出版日期: 2015-06-11

Corresponding Author(s): Wang Rui-Feng（王瑞峰）

引用本文:

. [J]. Frontiers of Physics, 2015, 10(3): 100305.
Wang Rui-Feng（王瑞峰）. A possible interplay between electron beams and magnetic fluxes in the Aharonov–Bohm effect. Front. Phys. , 2015, 10(3): 100305.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-015-0470-4
https://academic.hep.com.cn/fop/CN/Y2015/V10/I3/100305

1	P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, 1958
2	L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Nonrelativistic Theory), Beijing World Publishing Corporation, 1999
3	Y. Aharonov and D. Bohm, Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115(3), 485 (1959) https://doi.org/10.1103/PhysRev.115.485
4	R. G. Chambers, Shift of an electron interference pattern by enclosed magnetic flux, Phys. Rev. Lett. 5(1), 3 (1960) https://doi.org/10.1103/PhysRevLett.5.3
5	A. Tonomura, N. Osakabe, T. Matsuda, T. Kawasaki, J. Endo, S. Yano, and H. Yamada, Evidence for Aharonov–Bohm effect with magnetic field completely shielded from electron wave, Phys. Rev. Lett. 56(8), 792 (1986) https://doi.org/10.1103/PhysRevLett.56.792
6	Y. Aharonov and D. Bohm, Further considerations on electromagnetic potentials in the quantum theory, Phys. Rev. 123(4), 1511 (1961) https://doi.org/10.1103/PhysRev.123.1511
7	M. Peskin and A. Tonomura, The Aharonov–Bohm effect, Berlin: Springer-Verlag, 1989 https://doi.org/10.1007/BFb0032076
8	E. L. Feinberg, On the “special role” of the electromagnetic potentials in quantum mechanics, Sov. Phys. Usp. 5(5), 753 (1963) https://doi.org/10.1070/PU1963v005n05ABEH003453
9	H. Erlichson, Aharonov–Bohm effect — Quantum effects on charged particles in field-free regions, Am. J. Phys. 38(2), 162 (1970) https://doi.org/10.1119/1.1976266
10	R. F. Wang, An experimental scheme to verify the dynamics of the Aharonov–Bohm effect, Chin. Phys. B 18(8), 3226 (2009) https://doi.org/10.1088/1674-1056/18/8/022
11	R. F. Wang, Influence of induced charges in the electric Aharonov–Bohm effect, arXiv: 1409.6793, 2014
12	W. H. Furry and N. F. Ramsey, Significance of potentials in quantum theory, Phys. Rev. 118(3), 623 (1960) https://doi.org/10.1103/PhysRev.118.623
13	L. Vaidman, Role of potentials in the Aharonov–Bohm effect, Phys. Rev. A 86(4), 040101 (2012) https://doi.org/10.1103/PhysRevA.86.040101
14	V. B. Braginsky and F. Y. Khalili, Quantum Measurement, Cambridge University Press, 1992 https://doi.org/10.1017/CBO9780511622748
15	J. von Neumann, Mathematical Foundation of Quantum Mechanics, translated by R. T. Beyer, Princeton University Press, 1955
16	B. Liebowitz, Significance of the Aharonov–Bohm effect, Nuovo Cim. 38(2), 932 (1965) https://doi.org/10.1007/BF02748608
17	T. H. Boyer, Does the Aharonov–Bohm effect exist? Found. Phys. 30(6), 893 (2000) https://doi.org/10.1023/A:1003602524894
18	A. Caprez, B. Barwick, and H. Batelaan, Macroscopic test of the Aharonov–Bohm effect, Phys. Rev. Lett. 99(21), 210401 (2007) https://doi.org/10.1103/PhysRevLett.99.210401
19	M. Tinkham, Introduction to Superconductivity, New York: McGraw-Hill, Inc., 1996
20	Deaver and W. M. Fairbank, Experimental evidence for quantized flux in superconducting cylinders, Phys. Rev. Lett. 7(2), 43 (1961) https://doi.org/10.1103/PhysRevLett.7.43
21	N. Byers and C. N. Yang, Theoretical considerations concerning quantized magnetic flux in superconducting cylinders, Phys. Rev. Lett. 7(2), 46 1961) https://doi.org/10.1103/PhysRevLett.7.46
22	A. Tonomura, Direct observation of thitherto unobservable quantum phenomena by using electrons, Proc. Natl. Acad. Sci. USA 102(42), 14952 (2005) https://doi.org/10.1073/pnas.0504720102
23	A. Tonomura, Quantum phenomena visualized by electron waves, Int. J. Mod. Phys. B 21(32), 5291 (2007) https://doi.org/10.1142/S021797920703837X
24	A. Tonomura, Applications of electron holography, Rev. Mod. Phys. 59(3), 639 (1987) https://doi.org/10.1103/RevModPhys.59.639
25	M. A. Biondi, A. T. Forrester, M. P. Garfunkel, and C. B. Satterthwaite, Experimental evidence for an energy gap in superconductors, Rev. Mod. Phys. 30, 1109 (1958) https://doi.org/10.1103/RevModPhys.30.1109
26	W. H. Louisell, Quantum Statistical Properties of Radiation, John Wiley & Sons, Inc., 1990

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