标题： 非厄米量子系统的谱相位评估通过复数和奇异值 显示英文标题

标题： Assessment of spectral phases of non-Hermitian quantum systems through complex and singular values

摘要： 非厄米系统的混沌行为或缺乏混沌行为通常通过相关复特征值的谱分析来诊断。 最近，相关非厄米系统的奇异值被提出作为研究耗散量子混沌的有效度量。 受非厄米幂律带状随机矩阵丰富性质及其作为研究非厄米系统中局域化和扩展相位平台的前景的启发，我们进行了深入研究，通过复特征值和奇异值的视角来评估这些矩阵的不同谱相。 值得注意的是，复谱和奇异值分析的结果似乎不同，因此在识别不同相时需要谨慎。 我们还通过研究具有复位点无序的非厄米哈密顿量来举例说明我们的发现。 我们的工作表明，当哈密顿量的厄米部分和非厄米部分都存在无序时，这些系统对用于研究量子混沌的具体诊断工具非常敏感。 显示英文摘要

摘要： Chaotic behavior or lack thereof in non-Hermitian systems is often diagnosed via spectral analysis of associated complex eigenvalues. Very recently, singular values of the associated non-Hermitian systems have been proposed as an effective measure to study dissipative quantum chaos. Motivated by the rich properties of non-Hermitian power-law banded random matrices and its promise as a platform to study localized and delocalized phases in non-Hermitian systems, we make an in-depth study to assess different spectral phases of these matrices through the lens of both complex eigenvalues and singular values. Remarkably, the results from complex spectra and singular value analysis are seemingly different, thereby necessitating caution while identifying different phases. We also exemplify our findings by studying a non-Hermitian Hamiltonian with a complex on-site disorder. Our work indicates that systems, where disorder is present both in the Hermitian and non-Hermitian segments of a Hamiltonian, are sensitive to the specific diagnostic tool that needs to be employed to study quantum chaos.