标题： 一个无限的介观电阻网格：对弹道导电的探究与可视化 显示英文标题

标题： An infinite grid of mesoscopic resistors: investigation and visualization of ballistic conduction

摘要： 考虑了一个介观电阻器的正方形晶格。 每个键被建模为一条窄波导，而结点是由散射矩阵\mathbf{S}给出的弹性散射源。 通过详细地使用对称性和幺正性约束来简化所有可能的矩阵\mathbf{S}。 确定并可视化了系统在示例参数下的能量带结构。 连接附加到两个任意节点上的外部电极之间的电导由 Landauer 公式给出。 因此计算了电极之间的透射率。 论文的其余部分用于研究从一个电极注入电子后产生的波函数模式。 观察到，根据其能量，会出现钝化和局域化或复杂和扩展的模式。 从数学上证明了将电子能量适配到能带中可以与复杂模式的出现相关联。 最后，简要提到了所考虑模型的可能实验实现。 显示英文摘要

摘要： A square lattice of mesoscopic resistors is considered. Each bond is modeled as a narrow waveguide, while junctions are sources of elastic scattering given by a scattering matrix \mathbf{S}. Symmetry and unitarity constraints are used in a detailed way to simplify all possible matrices \mathbf{S}. Energetic band structure of the system is determined and visualized for exemplary parameters. Conductance between external electrodes attached to two arbitrary nodes is given by the Landauer formula. Thus the transmittance between the electrodes is calculated. The rest of the paper is devoted to studying wave function patterns arising from an electron injected through one electrode into the system. It is observed that depending on its energy both dull and localized or intricate and expansive patterns occur. It is justified mathematically that fitting electron energy into an energy band can be associated with emergence of complex patterns. Finally, possible experimental realizations of the considered model are briefly mentioned.