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'.
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