On the spectrum of a bent chain graph
On the spectrum of a bent chain graph
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在弯曲链图的谱上
DOI：
10.1088/1751-8113/41/41/415206
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Ondřej Turek
中科院分区：
文献类型：
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作者：
P. Duclos;P. Exner;Ondřej Turek
研究了链形无限量子图上的薛定谔算子，该图由在接触点处通过带参数的δ-耦合连接的全同环组成。如果图是“直的”，即相对于环位移是周期性的，则它的哈密顿量具有带谱，当α = 0时，所有的能隙都是开放的。我们认为一个“弯曲”变形的链组成的改变一个位置在一个单一的环，并表明，它会引起本征值在开放的光谱间隙。我们分析了这些特征值对耦合α和“弯曲角”的依赖性以及来自弯曲的系统的共振。我们还讨论了本征值和共振的光谱带的边缘处的行为。
We study Schrödinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by δ-couplings with a parameter . If the graph is ‘straight’, i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum with all the gaps open whenever α ≠ 0. We consider a ‘bending’ deformation of the chain consisting of changing one position at a single ring and show that it gives rise to eigenvalues in the open spectral gaps. We analyze dependence of these eigenvalues on the coupling α and the ‘bending angle’ as well as resonances of the system coming from the bending. We also discuss the behaviour of the eigenvalues and resonances at the edges of the spectral bands.