Bound states in bent soft waveguides

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.’