论文标题
无序相互作用的非热系统的光谱特性
Spectral Properties of Disordered Interacting Non-Hermitian Systems
论文作者
论文摘要
近年来，非热门系统引起了很大的兴趣。但是，这种系统中混乱和本地化的概念尚未达到与Hermitian系统相同的成熟度。在这里，我们考虑了非热相互作用的哈密顿量，并试图通过最近引入的光谱形式的非热类似物和复杂的间距比分析其混乱行为或缺乏这种行为。我们考虑了三种广泛相关的非热模型，它们在其方式方面是独特的，并作为此类调查的出色平台。考虑的两个模型是短距离的，具有不同的对称性。第三个模型是长期以来的，他的冬宫对应物本身已成为日益增长的兴趣的主题。所有这些模型都与相对较弱的疾病的相应对称类别的非热序随机矩阵理论呈现深厚的联系。在相对较强的障碍下，模型显示出与泊松统计相对应的复杂特征值相关性。我们的彻底分析预计将在理解无序的开放量子系统中发挥关键作用。
Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian interacting disordered Hamiltonians and attempt to analyze their chaotic behavior or lack of it through the lens of the recently introduced non-hermitian analog of the spectral form factor and the complex spacing ratio. We consider three widely relevant non-hermitian models which are unique in their ways and serve as excellent platforms for such investigations. Two of the models considered are short-ranged and have different symmetries. The third model is long-ranged, whose hermitian counterpart has itself become a subject of growing interest. All these models exhibit a deep connection with the non-hermitian Random Matrix Theory of corresponding symmetry classes at relatively weak disorder. At relatively strong disorder, the models show the absence of complex eigenvalue correlation, thereby, corresponding to Poisson statistics. Our thorough analysis is expected to play a crucial role in understanding disordered open quantum systems in general.
