Tunneling in soft waveguides: closing a book

0584754 - ÚJF 2025 RIV GB eng J - Journal Article
Exner, Pavel - Spitzkopf, David
Tunneling in soft waveguides: closing a book.
Journal of Physics A-Mathematical and Theoretical. Roč. 57, č. 12 (2024), č. článku 125301. ISSN 1751-8113. E-ISSN 1751-8121
R&D Projects: GA ČR(CZ) GA21-07129S
EU Projects: European Commission(XE) 873071 - SOMPATY
Research Infrastructure: e-INFRA CZ II - 90254
Institutional support: RVO:61389005
Keywords : quantum waveguides * Schrodinger operators * ditch-shaped potentials * discrete spectrum * tunneling effect
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.1, year: 2022
Method of publishing: Open access
https://doi.org/10.1088/1751-8121/ad2c80

We investigate the spectrum of a soft quantum waveguide in two dimensions of the generalized 'bookcover' shape, that is, Schrodinger operator with the potential in the form of a ditch consisting of a finite curved part and straight asymptotes which are parallel or almost parallel pointing in the same direction. We show how the eigenvalues accumulate when the angle between the asymptotes tends to zero. In case of parallel asymptotes the existence of a discrete spectrum depends on the ditch profile. We prove that it is absent in the weak-coupling case, on the other hand, it exists provided the transverse potential is strong enough. We also present a numerical example in which the critical strength can be assessed.
Permanent Link: https://hdl.handle.net/11104/0352599