Abstract We consider the Aharonov-Bohm magnetic potential and study the transition from normal to superconducting solutions within the Ginzburg-Landau model of superconductivity. We obtain oscillatory patterns which are consistent with the Little-Parks effect. We study also the same problem but for a regularization of the Aharonov-Bohm potential, which leads to an interesting Aharonov-Bohm like magnetic field, and we prove that the transition between superconducting and normal solutions is not monotone too. Our results explore a mechanism to derive the Aharonov-Bohm magnetic potential starting from a step magnetic field, thereby presenting a new aspect of magnetic steps, besides their favoring of the celebrated edge states.

中文翻译：

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由 Aharonov-Bohm 势驱动的 Ginzburg-Landau 模型中的振荡模式

摘要 我们考虑了 Aharonov-Bohm 磁势，并研究了 Ginzburg-Landau 超导模型内从正常解到超导解的转变。我们获得了与小公园效应一致的振荡模式。我们也研究了同样的问题，但对 Aharonov-Bohm 势进行了正则化，这导致了一个有趣的 Aharonov-Bohm 样磁场，并且我们证明了超导和正常解之间的转变也不是单调的。我们的结果探索了一种从阶跃磁场开始推导出 Aharonov-Bohm 磁势的机制，从而呈现出磁阶跃的新方面，除了它们有利于著名的边缘状态。