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arXiv · 2007.10946

Soft quantum waveguides with an explicit cut-locus

Sylwia Kondej·David Krejcirik·Jan Kriz
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Abstract

We consider two-dimensional Schroedinger operators with an attractive potential in the form of a channel of a fixed profile built along an unbounded curve composed of a circular arc and two straight semi-lines. Using a test-function argument with help of parallel coordinates outside the cut-locus of the curve, we establish the existence of discrete eigenvalues. This is a special variant of a recent result of Exner in a non-smooth case and via a different technique which does not require non-positive constraining potentials.

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Sylwia Kondej, David Krejcirik, Jan Kriz. 2020-07-21. Soft quantum waveguides with an explicit cut-locus. https://doi.org/10.1088/1751-8121/abf05e

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