Convergence of resonances on thin branched quantum waveguides | Zendy

Pavel Exner | Zendy; Olaf Post | Zendy

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Convergence of resonances on thin branched quantum waveguides

Author(s) -

Pavel Exner,

Olaf Post

Publication year - 2007

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.2749703

Subject(s) - resolvent , hilbert space , quantum graph , mathematics , quantum , convergence (economics) , scaling , laplace operator , mathematical analysis , graph , pure mathematics , quantum mechanics , physics , discrete mathematics , geometry , economics , economic growth

We prove an abstract criterion stating resolvent convergence in the case ofoperators acting in different Hilbert spaces. This result is then applied tothe case of Laplacians on a family $X_\eps$ of branched quantum waveguides.Combining it with an exterior complex scaling we show, in particular, that theresonances on $X_\eps$ approximate those of the Laplacian with ``free''boundary conditions on $X_0$, the skeleton graph of $X_\eps$.Comment: 48 pages, 1 figur

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