Year: 2023
Type: preprint
Abstract: The aim of this paper is to show that a two-dimensional Schrödinger 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'.
Source: arXiv (Cornell University)
Authors: Exner, Pavel, Vugalter, Semjon
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4367628173