薄畴极限与强抗磁性的反例
Thin domain limit and counterexamples to strong diamagnetism
摘要：
研究了均匀磁场作用下薄平面光滑管状区域中的磁拉普拉斯算子和Ginzburg-Landau泛函。我们给出了强抗磁性的反例，并由此证明了从超导态到正常态的跃迁是非单调的。在某些非线性区域，我们确定了序参量的结构，并计算了沿样品边界的超电流。我们的结果是在协议中观察到的Little-Parks实验中，一个薄的圆柱形样品。
英文摘要：
We study the magnetic Laplacian and the Ginzburg-Landau functional in a thin planar, smooth, tubular domain and with a uniform applied magnetic field. We provide counterexamples to strong diamagnetism, and as a consequence, we prove that the transition from the superconducting to the normal state is non-monotone. In some non-linear regime, we determine the structure of the order parameter and compute the super-current along the boundary of the sample. Our results are in agreement with what was observed in the Little-Parks experiment, for a thin cylindrical sample.
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