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arXiv · 1110.1843

New application of decomposition of U(1) gauge potential:Aharonov-Bohm effect and Anderson-Higgs mechanism

Jian-Feng Li·Yu Jiang·Wei-Min Sun·Hong-Shi Zong·Fan Wang
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Abstract

In this paper we study the Aharonov-Bohm (A-B) effect and Anderson-Higgs mechanism in Ginzburg-Landau model of superconductors from the perspective of the decomposition of U(1) gauge potential. By the Helmholtz theorem, we derive exactly the expression of the transverse gauge potential $\vec{A}_\perp$ in A-B experiment, which is gauge-invariant and physical. For the case of a bulk superconductor, we find that the gradient of the total phase field $θ$ provides the longitudinal component ${\vec A}_{\parallel}$, which reflects the Anderson-Higgs mechanism. For the case of a superconductor ring, the gradient of the longitudinal phase field $θ_1$ provides the longitudinal component ${\vec A}_{\parallel}$, while the transverse phase field $θ_2$ produces new physical effects such as the flux quantization inside a superconducting ring.

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Jian-Feng Li, Yu Jiang, Wei-Min Sun, Hong-Shi Zong, Fan Wang. 2012-05-29. New application of decomposition of U(1) gauge potential:Aharonov-Bohm effect and Anderson-Higgs mechanism. https://doi.org/10.1142/s0217984912501242

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