23-32 Pavel Exner and Semjon Vugalter
Bound states in bent soft waveguides (535K, pdf) May 1, 23
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Abstract. The aim of this paper is to show that a two-dimensional Schr dinger 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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