量子图的拓扑共振
Topological Resonances on Quantum Graphs
摘要：
本文试图将Smilansky等人关于“拓扑共振”的结果在数学基础上加以推广，指出存在紧支撑本征函数的度量集在量子图实轴附近共振的渐近性中起着关键作用.我们给出了这个半代数集的维数的几个估计，特别是图的围长。树的情况也进行了讨论。
英文摘要：
In this paper, we try to put the results of Smilansky and al. on "Topological resonances" on a mathematical basis.A key role in the asymptotic of resonances near the real axis for Quantum Graphs is played by the set of metrics for which there exists compactly supported eigenfunctions. We give several estimateof the dimension of this semi-algebraic set, in particular in terms of the girth of the graph. The case oftrees is also discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
