标题： 复频谱指纹：基本概念和理论 显示英文标题

标题： Complex Frequency Fingerprint: Basic Concept and Theory

摘要： 我们引入了复频指纹（CFF），这是一种实验上可实现的方法，用于检测复频格林函数（GF）。 与实频GF不同，其中$\omega$是实数，这种复频GF在非厄米和量子多体系统中被证明起着必要作用。 对于非厄米系统，我们将证明我们的方法能够检测复频能谱、本征态和复频GF，贯穿整个复平面，提供对非厄米皮肤效应的必要识别。 对于量子多体系统，我们的方法揭示了复平面上的准粒子峰，并直观地展示了相互作用效应。 这些信息难以通过实频检测获得。 我们的方法为探索非厄米和量子多体系统中的奇异现象铺平了道路，跨越了不同物理领域的理论与实验。 显示英文摘要

摘要： We introduce the complex frequency fingerprint (CFF), an experimentally accessible method for detecting the complex frequency Green's function (GF). Unlike the real frequency GF, where $\omega$ is real, this complex frequency GF is shown to play a necessary role in both non-Hermitian and quantum many-body systems. For non-Hermitian systems, we will prove that our method detects complex energy spectra, eigenstates, and complex frequency GFs throughout the complex plane, providing necessary identification of the non-Hermitian skin effect. For quantum many-body systems, our method reveals quasiparticle peaks across the complex plane and intuitively illustrates interaction effects. This information is difficult to obtain with real frequency detection. Our method paves the way for exploring exotic phenomena in both non-Hermitian and quantum many-body systems, bridging theory and experiment across diverse physical areas.