标题： 超对称的位移记忆效应 显示英文标题

标题： Displacement Memory Effect from Supersymmetry

摘要： 我们使用超对称量子力学解释平面引力波的位移记忆效应（DME）的最新结果。这种新方法源于测地线方程和薛定谔方程都是斯特姆-刘维勒边值问题。超对称为Pöschl-Teller和Scarf型提供了统一的框架，并自然地得到了与DME相关的波幅临界值。在我们的框架中，我们得到了一个关于超势渐近值和测地线的DME紧凑公式。此外，这种新技术使我们能够利用超伙伴势构建具有2个横向方向的平面和引力波。最后，我们研究了一种受超对称量子力学启发的奇异波形中的DME，这表明了我们方法的更广泛应用性。 显示英文摘要

摘要： We explain the recent results on the displacement memory effect (DME) of plane gravitational waves using supersymmetric quantum mechanics. This novel approach stems from that both the geodesic and the Schr\"odinger equations are Sturm-Liouville boundary value problems. Supersymmetry provides a unified framework for the P\"oschl-Teller and the Scarf profiles and yields the critical values of the associated wave amplitudes for DME in a natural way. Within our framework, we obtain a compact formula for DME in terms of the asymptotic values of the superpotential and the geodesics. In addition, this new technique enables us to build plane and gravitational waves with 2-transverse directions using superpartner potentials. Lastly, we study DME within a singular wave profile inspired by supersymmetric quantum mechanics, which demonstrates the broader applicability of our method.