Work

Soft quantum waveguides with an explicit cut-locus

Year: 2021

Type: article

Abstract: We consider two-dimensional Schrödinger 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 (2020 J. Phys. A: Math. Theor. 53 355302) in a non-smooth case and via a different technique which does not require non-positive constraining potentials.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/abf05e

Authors: Sylwia Kondej, David Krejčiřík, Jan Kříž

Institutions: University of Zielona Góra, Czech Technical University in Prague, University of Hradec Králové

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Grantová Agentura České Republiky

Award: New challenges for spectral theory: geometry, advanced materials and complex fields