Bound States in Bent Soft Waveguides
Spectral Theory
2023-12-25 v2 Mathematical Physics
math.MP
Quantum Physics
Abstract
The aim of this paper is to show that a two-dimensional Schr\"odinger operator with the potential in the form of a `ditch' of a fixed profile can have a geometrically induced discrete spectrum; this happens if such a potential channel has a single or multiple bends being straight outside a compact. Moreover, under stronger geometric restrictions the claim remains true in the presence of a potential bias at one of the channel `banks'.
Keywords
Cite
@article{arxiv.2304.14776,
title = {Bound States in Bent Soft Waveguides},
author = {Pavel Exner and Semjon Vugalter},
journal= {arXiv preprint arXiv:2304.14776},
year = {2023}
}
Comments
Revised version, to appear in J. Spectral Theory; 29 pages, four figures, some parts of the argument made more detailed