作为Koopman算子整函数的共振交叉
Resonance crossings as entire functions of the Koopman operator
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中文总结 AI 辅助
本研究针对EMRI系统瞬态轨道共振处理难题，在Koopman算子层面提出新方法，通过克尔测地线数值验证，可恢复共振跃变的幅度与相位相关性。
中文摘要 AI 辅助
由恒星级致密天体与大质量黑洞组成的天体物理双星，是未来天基引力波探测器最具潜力的探测源之一。这些极端质量比旋进（EMRI）系统可被相干追踪超过$10^5$个轨道，编码了强场引力的详细信息。将探测结果转化为物理参数需要具备相当精度的模型，其中一个突出难题是瞬态轨道共振的处理。本研究在Koopman算子层面解决该问题，将波形提升为可观测量，一个径向周期的演化是线性算子。在交叉点处移除快时间尺度且无奇异性，取决于选择该算子的一个函数。我们在克尔测地线（由建模的驱动力项驱动穿过3:2交叉点）上验证该方法：标准近恒等变换的系数发散，而有限窗口生成元达到其解析界，精度优于$10^6$分之一；对两倍交叉时长取平均，可恢复共振跃变及其预测的幅度和相位相关性。
英文摘要
Astrophysical binaries formed by a stellar-mass compact object and a massive black hole are among the most promising sources for future space-based gravitational-wave detectors. These extreme mass-ratio inspiral (EMRI) systems are tracked coherently over more than $10^{5}$ orbits, encoding detailed information about strong-field gravity. Translating a detection into physical parameters requires models of comparable precision. One outstanding difficulty is the treatment of transient orbital resonances. In this work we address the problem at the level of the Koopman operator, where the waveform is promoted to an observable and the evolution over one radial cycle is a linear operator. Removing the fast timescale without a singularity at a crossing is then a matter of choosing a function of that operator. We demonstrate the approach on a Kerr geodesic driven through the 3:2 crossing by a modelled forcing term. There the coefficient of the standard near-identity transformation diverges, while the finite-window generator attains its analytic bound to better than one part in $10^{6}$. Averaging over twice the crossing duration recovers the resonant jump with its predicted magnitude and phase dependence.
