具有畴壁的狄拉克方程的色散估计
Dispersive Estimates for Dirac Operators with General Domain Walls: One and Two Dimensions
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中文总结 AI 辅助
研究具有有界和无界畴壁的二维狄拉克方程及类似一维问题的色散衰减估计，通过新方法分析超出常系数狄拉克算子局部扰动框架的模型，揭示拓扑等效模型动力学可能不同。
中文摘要 AI 辅助
我们建立了具有有界和无界畴壁的二维狄拉克方程以及类似一维问题的色散衰减估计。这些是拓扑绝缘体中体边对应关系的典型模型，但其色散动力学此前未被研究。我们表明拓扑等效模型可能表现出定性不同的动力学。我们的新方法使我们能够分析超出常系数狄拉克算子局部扰动通常框架的模型。
英文摘要
We establish dispersive decay estimates for two-dimensional Dirac equations with bounded and unbounded domain walls, together with estimates for the analogous one-dimensional problem. These are paradigmatic models of bulk-edge correspondence in topological insulators, yet their dispersive dynamics have not been previously studied. We show that topologically equivalent models may exhibit qualitatively different dynamics. Our new approach allows us to analyze models which are beyond the usual framework of localized perturbations of constant-coefficient Dirac operators.
