A phenomenon of splitting resonant-tunneling one-point interactions

摘要

The so-called delta'-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, continuously depending on the strength of this interaction. On the other hand, in several recent publications, the delta'-potential has been shown to be transparent at some 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 delta'-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 delta'-interaction and the resonant-tunneling point interactions is derived and the splitting of the resonance sets for tunneling plays a crucial role. (C) 2018 Elsevier Inc. All rights reserved.