Bound States in Bent Soft Waveguides

• URL: http://arxiv.org/abs/2304.14776v2
• Date: Fri, 22 Dec 2023 08:42:22 GMT
• Title: Bound States in Bent Soft Waveguides
• Authors: Pavel Exner and Semjon Vugalter
• Abstract summary: 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. The claim remains true in the presence of a potential bias at one of the channel banks'
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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'.

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