Convergence of resonances on thin branched quantum wave guides

Details Convergence of resonances on thin branched quantum wave guides Convergence of resonances on thin branched quantum wave guides

2007-02-21

arxiv.org/abs/math-ph/0702075v1

Physics

Mathematical Physics

48 pages, 1 figure

Scientific paper

10.1063/1.2749703

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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