多个奇异界面附近的边缘态传播
Edge State Propagation Near Multiple and Singular Interfaces
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中文总结 AI 辅助
研究二维狄拉克算子边缘态半经典传播，针对质量零集构成的不相交界面和奇异界面，分别证明波包局限情况、量化距离影响，确定波包近似有效区域及估计失去一致性的尺度。
中文摘要 AI 辅助
我们研究具有空间变化质量的二维狄拉克算子边缘态的半经典传播。质量的零集模拟拓扑相之间的界面，它可以由两条不相交的光滑曲线组成或者有一个孤立奇点。对于不相交界面，我们证明了最初局域在一个分量上的波包在长半经典时间尺度上仍局限在该界面附近，并量化了两个分量之间距离对近似精度的影响。对于奇异界面，我们确定了波包近似在接近奇点时仍然有效的区域，并确定了估计失去一致性的尺度。
英文摘要
We study the semiclassical propagation of edge-states for a two-dimensional Dirac operator with a spatially varying mass. The zero set of the mass models the interface between topological phases and is allowed either to consist of two disjoint smooth curves or to possess an isolated singular point. For disjoint interfaces, we prove that a wave packet initially localized on one component remains confined near this interface over long semiclassical time scales and we quantify the influence of the distance between the two components on the accuracy of the approximation. For singular interfaces, we determine the regime in which the wave-packet approximation remains valid as the packet approaches the singularity and identify the scaling at which our estimates lose their uniformity.
