细分支量子波导上共振态的收敛性
Convergence of resonances on thin branched quantum wave guides
摘要：
我们证明了一个抽象的标准，说明预解收敛的情况下，运营商在不同的希尔伯特空间。然后将这一结果应用于分支量子波导族$X_\eps$上的拉普拉斯算子的情形。结合它与外部复杂的缩放，我们表明，特别是，$X_\eps$上的共振近似的拉普拉斯算子与“自由”的边界条件上的$X_0$，骨架图的$X_\eps$。
英文摘要：
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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