标题： 磁象上的跳蚤 显示英文标题

标题： The Flea on the Magnetic Elephant

摘要： 我们研究了一个具有两个径向对称磁井的二维磁拉普拉斯算子。其谱性质由它们之间的隧穿效应决定。如果隧穿效应很弱且磁井呈镜面对称，则两个最低的特征函数会在两个磁井中都有分布，大致相等。在这篇短文中，我们证明在这种情况下，一个极小的对称性破坏可以产生显著影响，使得每个特征函数主要局限于其中一个磁井内。这类似于薛定谔算子中的“大象身上的跳蚤”效应；我们的结果显示它有一个纯粹的磁性对应物。 显示英文摘要

摘要： We investigate a two-dimensional magnetic Laplacian with two radially symmetric magnetic wells. Its spectral properties are determined by the tunneling between them. If the tunneling is weak and the wells are mirror symmetric, the two lowest eigenfunctions are localized in both wells being distributed roughly equally. In this note we show that an exponentially small symmetry violation can in this situation have a dramatic effect, making each of the eigenfunctions localized dominantly in one well only. This is reminiscent of the `flea on the elephant' effect for Schr\"odinger operators; our result shows that it has a purely magnetic counterpart.