Soft quantum waveguides with an explicit cut-locus
Mathematical Physics
2022-08-22 v1 math.MP
Spectral Theory
Quantum Physics
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.
Cite
@article{arxiv.2007.10946,
title = {Soft quantum waveguides with an explicit cut-locus},
author = {Sylwia Kondej and David Krejcirik and Jan Kriz},
journal= {arXiv preprint arXiv:2007.10946},
year = {2022}
}
Comments
8 pages, 3 figures