发表机构
CENTRA, Departamento de Física, Instituto Superior Técnico – IST, Universidade de Lisboa – UL; University of Copenhagen（里斯本大学高级技术研究所物理系CENTRA; 哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用双Pöschl-Teller模型解析地揭示谱不稳定性在时域中表现为首个回波后的线性时间修正，可视为拟正规模式频率移动，并通过数值模拟验证。
AI 中文摘要
我们利用一维双Pöschl-Teller模型研究了谱不稳定性对时域波形的影响。通过解析地追踪主势垒与一个弱、空间分离的微扰之间的连续散射，我们识别出一个在势垒间一次因果往返后首次出现的长期贡献。在第一个回波之前，所有泛音都保持其未受扰动的频率。当第一个回波到达观测者后，存在一个线性的、随时间增长的修正。当该修正为微扰时，可解释为拟正规模式频率的移动。在这种情况下，我们证明其系数重现了频域结果。更一般地，它产生有限时间有效频率，这些频率不必与未受扰动或完全受扰动的拟正规模式谱一致。我们通过数值时域演化证实了我们的解析计算结果。
英文摘要
We investigate the effect of a spectral instability on the time domain waveform using a one-dimensional double Pöschl-Teller model. By analytically following successive scatterings between the primary potential barrier and a weak, spatially separated perturbation, we identify a secular contribution that first appears after one causal round trip between the barriers. Before the first echo, all overtones remain at their unperturbed frequencies. After the first echo reaches the observer, there is a secular, linear-in-time correction. When this correction is perturbative, it can be interpreted as a shift of the quasinormal mode frequency. In that case, we show that its coefficient reproduces the frequency-domain result. More generally, it generates finite-time effective frequencies that need not coincide with either the unperturbed or fully perturbed quasi-normal mode spectrum. We confirm the results of our analytic calculation using numerical time-domain evolutions.
Comments10 pages (plus 5 pages appendix), 8 figures
