共振隧穿单点相互作用的分裂现象
A phenomenon of splitting resonant-tunneling one-point interactions
摘要：
所谓的$δ'$ -相互作用作为一个特殊的例子，在Kurasov的分布理论上开发的空间上的不连续（在奇点）的测试功能，是确定的对角传输矩阵，{ \em连续}取决于这种相互作用的强度。另一方面，在一些最近的出版物中，$δ'$ -势已被证明在强度常数的某些{ \em离散}值处是透明的，而超过这些值则是不透明的。这种矛盾在这里解决了简单的物理例子，即异质结构由两个非常薄的层由无穷小的距离分开。在三尺度压缩极限下，当层间距离和层厚同时趋于零时，实现了各种各样的单点相互作用。关键点是推广的$δ'$ -相互作用的家庭的共振集出现在一个可数的连续的二维曲线的形式。由此导出了Kurasov $δ'$相互作用与共振隧穿点相互作用之间的联系，并指出共振集的分裂对隧穿起着至关重要的作用。
英文摘要：
The so-called $δ'$-interaction as a particular example in Kurasov's distribution theory developed on the space of discontinuous (at the point of singularity) test functions, is identified with the diagonal transmission matrix, {\em continuously} depending on the strength of this interaction. On the other hand, in several recent publications, the $δ'$-potential has been shown to be transparent at some {\em discrete} values of the strength constant and opaque beyond these values. This discrepancy is resolved here on the simple physical example, namely the heterostructure consisting of two extremely thin layers separated by infinitesimal distance. In the three-scale squeezing limit as the thickness of the layers and the distance between them simultaneously tend to zero, a whole variety of single-point interactions is realized. The key point is the generalization of the $δ'$-interaction to the family for which the resonance sets appear in the form of a countable number of continuous two-dimensional curves. In this way, the connection between Kurasov's $δ'$-interaction and the resonant-tunneling point interactions is derived and the splitting of the resonance sets for tunneling pla ys a crucial role.
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