BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pavel Exner (Doppler Institute for Mathematical Physics and Applie d Mathematics) DTSTART:20201110T134500Z DTEND:20201110T144500Z DTSTAMP:20260412T205522Z UID:qc_seminar/1 DESCRIPTION:Title: Spiral quantum wavegudies\nby Pavel Exner (Doppler Institute for Ma thematical Physics and Applied Mathematics) as part of Quantum Circle\n\n\ nAbstract\nThe topic of this talk is a quantum particle confined to a spir al-shaped region with Dirichlet boundary. As a case study we analyze in de tail the Archimedean spiral and show that the spectrum above the continuum threshold is absolutely continuous away from the thresholds. The subtle d ifference between the radial and perpendicular width implies\, however\, t hat in contrast to numerous examples of `less curved' waveguides\, the dis crete spectrum is empty in this case. We also discuss modifications such a multi-arm Archimedean spirals and spiral waveguides with a central cavity \; in the latter case bound state already exist if the cavity exceeds a cr itical size. For spiral regions of a more general type the spectral nature depends substantially on whether their coil width is `expanding' or `shri nking'. The most interesting situation occurs in the case we call asymptot ically Archimedean\, where the existence of bound states depends on the di rection from which the asymptotics is reached.\n LOCATION:https://researchseminars.org/talk/qc_seminar/1/ END:VEVENT END:VCALENDAR