Contact interactions on graph superlattices
Contact interactions on graph superlattices
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图超晶格上的接触相互作用
DOI：
10.1088/0305-4470/29/1/011
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
P. Exner
中科院分区：
文献类型：
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作者：
P. Exner
我们考虑一个量子力学粒子生活在一个图，并讨论其波函数在图的顶点的行为。除了标准的（或型）边界条件与连续波函数，我们调查两种类型的奇异耦合是类似的相互作用和对称化版本的粒子在一条线上。我们表明，这些耦合可以用来模拟图形超晶格中的点结取代复杂的几何散射。我们还讨论了具有上述耦合的矩形晶格的能带谱。我们表明，他们大致对应于他们的Kronig-Penney类似物：晶格的带的宽度是渐近有界的，不接近零，而晶格间隙的宽度有界。然而，如果晶格间距比是一个无理数，很难近似的有理数，耦合常数足够小，晶格没有超过阈值的频谱间隙。另一方面，在耦合常数的临界值以上会出现无限多的间隙;对于几乎所有的比率，这个值都是零。
We consider a quantum mechanical particle living on a graph and discuss the behaviour of its wavefunction at graph vertices. In addition to the standard (or -type) boundary conditions with continuous wavefunctions, we investigate two types of a singular coupling which are analogous to the interaction and its symmetrized version for a particle on a line. We show that these couplings can be used to model graph superlattices in which point junctions are replaced by complicated geometric scatterers. We also discuss the band spectra for rectangular lattices with the mentioned couplings. We show that they roughly correspond to their Kronig - Penney analogues: the lattices have bands whose widths are asymptotically bounded and do not approach zero, while the lattice gap widths are bounded. However, if the lattice-spacing ratio is an irrational number badly approximable by rationals, and the coupling constant is small enough, the lattice has no gaps above the threshold of the spectrum. On the other hand, infinitely many gaps emerge above a critical value of the coupling constant; for almost all ratios this value is zero.
DOI：
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发表时间：
2004
期刊：
Kyushu Journal of Mathematics 58
影响因子：
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作者：
H.Kazama;K.N.Kim
通讯作者：
K.N.Kim
T.Kataoka：“通过光散射法直接观察 KCI 晶体中的滑移位错”应用物理快报。
DOI：
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