Convergence of resonances on thin branched quantum wave guides
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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) | ||
Credits: |
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Explicit content: | No | ||
Aspect Ratio: | 4:3 | ||
Screencast: | No | ||
Bumper: | /sms-ingest/static/new-4x3-bumper.dv | ||
Trailer: | /sms-ingest/static/new-4x3-trailer.dv |
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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