- 07-46 Pavel Exner and Olaf Post
- Convergence of resonances on thin branched quantum wave guides
Feb 26, 07
(auto. generated ps),
of related papers
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 $X_\eps$.