Soft quantum waveguides with an explicit cut-locus

• URL: http://arxiv.org/abs/2007.10946v1
• Date: Tue, 21 Jul 2020 17:03:07 GMT
• Title: Soft quantum waveguides with an explicit cut-locus
• Authors: Sylwia Kondej, David Krejcirik, Jan Kriz
• Abstract summary: 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. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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