图逼近与全局结构的涌现
Approximations by graphs and emergence of global structures
摘要：
我们研究台球系统的近似格图。它表明，在自然的假设下，图形波函数近似的薛定谔方程的能量重新标度的台球尺寸的解决方案。作为一个例子，我们分析了西奈台球附带的线索。结果表明，出现在大型量子图的全球结构，并提供有趣的比较，在复杂的网络中观察到的模式不同的性质。
英文摘要：
We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wavefunctions approximate solutions of the Schroedinger equation with energy rescaled by the billiard dimension. As an example, we analyze a Sinai billiard with attached leads. The results illustrate emergence of global structures in large quantum graphs and offer interesting comparisons with patterns observed in complex networks of a different nature.
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