Bound states in bent soft waveguides
Pavel Exner
Czech Technical University, Prague, Czechia; Academy of Sciences, Řež near Prague, CzechiaSemjon Vugalter
Karlsruhe Institute of Technology, Karlsruhe, Germany
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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 occurs 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.’
Cite this article
Pavel Exner, Semjon Vugalter, Bound states in bent soft waveguides. J. Spectr. Theory 14 (2024), no. 2, pp. 427–457
DOI 10.4171/JST/502