论文标题

沿曲面壁的半经典传播

Semiclassical propagation along curved domain walls

论文作者

Bal, Guillaume

论文摘要

我们分析了二维色散和相对论的波袋的传播,该波袋位于零水平的附近设置域壁的$γ$。我们认为的主要应用是拓扑非平凡的狄拉克模型和类似但拓扑的klein-gordon方程。静态域壁模拟了一个界面,将两个绝缘介质的界面分开,可能不同。我们提出了波袋的半经典振荡表示,并估算了它们在适当的能量规范中的准确性。我们描述了沿$γ$的相对论模式的传播,并通过固定相位方法分析色散模式。在没有转折点的情况下,我们表明任意局部和光滑的初始条件可以表示为这种波袋的叠加。在存在转折点的情况下,结果仅适用于足够高频的波袋。

We analyze the propagation of two-dimensional dispersive and relativistic wavepackets localized in the vicinity of the zero level set $Γ$ of a domain wall. The main applications we consider are a topologically non-trivial Dirac model and a similar but topologically trivial Klein-Gordon equation. The static domain wall models an interface separating two insulating media in possibly different topological phases. We propose a semiclassical oscillatory representation of the wavepackets and provide an estimate of their accuracy in appropriate energy norms. We describe the propagation of relativistic modes along $Γ$ and analyze dispersive modes by a stationary phase method. In the absence of turning points, we show that arbitrary localized and smooth initial conditions may be represented as a superposition of such wavepackets. In the presence of turning points, the results apply only for sufficiently high-frequency wavepackets.

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