Abstract
When a hard-wall tube is bent, a quantum particle confined to it can exhibit localized states. This is demonstrated for tubes in two and three dimensions. The effect is robust, it can occur even if the bend is not smooth as well as due to various other geometric perturbations. For thin tubes, the motion is essentially one-dimensional with an effective potential determined by the tube curvature. On the other hand, twisting of a tube with a non-circular cross section has an opposite effect, it can prevent the existence of bound states.
Ad methodum philosophicam perdiscendam multum valet mathematica, et imprimis arithmetica et geometria.
Jan Amos Komenský, Orbis Pictus
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Exner, P., Kovařík, H. (2015). Geometrically Induced Bound States. In: Quantum Waveguides. Theoretical and Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-18576-7_1
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DOI: https://doi.org/10.1007/978-3-319-18576-7_1
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