Convergence of resonances on thin branched quantum wave guides
33 mins 14 secs,
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| Description: |
Post, O (Humboldt)
Monday 02 April 2007, 16:30-17:00 Quantum Graphs, their Spectra and Applications |
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| Created: | 2008-09-01 06:32 | ||
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| Collection: | Analysis on Graphs and its Applications | ||
| Publisher: | Isaac Newton Institute | ||
| Copyright: | Post, O | ||
| Language: | eng (English) | ||
| Distribution: |
World
(downloadable)
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| Explicit content: | No | ||
| Aspect Ratio: | 4:3 | ||
| Screencast: | No | ||
| Bumper: | UCS Default | ||
| Trailer: | UCS Default | ||
| Abstract: | We consider convergence results of a family of noncompact, thin branched quantum waveguides (QWG) to the associated quantum graph. The branched quantum waveguide can either be a thin neighbourhood of the (embedded) quantum graph or be defined as a manifold without boundary (like the surface of a pipeline network approaching the metric graph). On the QWG has boundary, we consider the (Neumann) Laplacian; on the metric graph we consider the Laplacian with free boundary conditions. Our main result is a convergence result for the spectrum and resonances under some natural uniformity conditions on the spaces. |
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