Spectral properties of spiral-shaped quantum waveguides

0538785 - ÚJF 2021 RIV GB eng J - Journal Article
Exner, Pavel - Tater, Miloš
Spectral properties of spiral-shaped quantum waveguides.
Journal of Physics A-Mathematical and Theoretical. Roč. 53, č. 50 (2020), č. článku 505303. ISSN 1751-8113. E-ISSN 1751-8121
Institutional support: RVO:61389005
Keywords : Dirichlet boundary * quantum waveguides * spiral-shaped regions
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.132, year: 2020
Method of publishing: Open access
https://doi.org/10.1088/1751-8121/abc5d3

We investigate properties of a particle confined to a hard-wall spiral-shaped region. As a case study we analyze in detail the Archimedean spiral for which the spectrum above the continuumthreshold is absolutely continuous away from the thresholds.The subtle difference between the radial and perpendicularwidth implies, however, that in contrast to the 'less curved' waveguides, the discrete spectrum is empty in this case. We also discuss modifications such as multiarm Archimedean spirals and spiral waveguides with a central cavity. In the latter case bound state already exist if the cavity radius exceeds a critical size. For more general spiral regions the spectral nature depends on whether they are 'expanding' or 'shrinking'. The most interesting situation occurs in the asymptotically Archimedean case where the existence of bound states depends on the direction from which the asymptotical value of width is reached.
Permanent Link: http://hdl.handle.net/11104/0316513