07-46 Pavel Exner and Olaf Post
Convergence of resonances on thin branched quantum wave guides (769K, ps) Feb 26, 07
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Abstract. We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family \$X_\eps\$ of branched quantum waveguides. Combining it with an exterior complex scaling we show, in particular, that the resonances on \$X_\eps\$ approximate those of the Laplacian with ``free'' boundary conditions on \$X_0\$, the skeleton graph of \$X_\eps\$.

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