English

A regular version of Smilansky model

Mathematical Physics 2019-12-10 v1 math.MP Spectral Theory Quantum Physics

Abstract

We discuss a modification of Smilansky model in which a singular potential `channel' is replaced by a regular, below unbounded potential which shrinks as it becomes deeper. We demonstrate that, similarly to the original model, such a system exhibits a spectral transition with respect to the coupling constant, and determine the critical value above which a new spectral branch opens. The result is generalized to situations with multiple potential `channels'.

Keywords

Cite

@article{arxiv.1308.4249,
  title  = {A regular version of Smilansky model},
  author = {Diana Barseghyan and Pavel Exner},
  journal= {arXiv preprint arXiv:1308.4249},
  year   = {2019}
}

Comments

LaTeX, 17 pages

R2 v1 2026-06-22T01:12:01.236Z