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We would like to invite you to the first seminar of Quantum Circle in November and the very first Quantum Circle seminar ONLINE. Through the Zoom platform will speak prof. RNDr. Pavel Exner, DrSc. (FJFI) on Spiral quantum waveguides. The seminar takes place on Tuesday, November 10, 2020 from 2.45 pm. The Zoom link, which will allow you to participate in the seminar, can be found on the Quantum Circle website.

The topic of this talk is a quantum particle confined to a spiral-shaped region with Dirichlet boundary. As a case study we analyze in detail the Archimedean spiral and show that the spectrum above the continuum threshold is absolutely continuous away from the thresholds. The subtle difference between the radial and perpendicular width implies, however, that in contrast to numerous examples of 'less curved' waveguides, the discrete 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 critical size. For spiral regions of a more general type the spectral nature depends substantially on whether their coil width is 'expanding' or 'shrinking'. The most interesting situation occurs in the case we call asymptotically Archimedean, where the existence of bound states depends on the direction from which the asymptotics is reached.

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