Random matrix theory of the isospectral twirling
Random matrix theory of the isospectral twirling
复制标题
DOI：
10.21468/scipostphys.10.3.076
复制
发表时间：
2020-12
期刊：
影响因子：
--
通讯作者：
Salvatore F. E. Oliviero;L. Leone;F. Caravelli;A. Hamma
中科院分区：
文献类型：
--
作者：
Salvatore F. E. Oliviero;L. Leone;F. Caravelli;A. Hamma
本文利用等谱旋转的概念，系统地研究了Hamilton算子等谱系综的动力学性质，拓展了文献[1]的研究范围和方法。[1]的文件。哈密顿量的相关集合是由显着谱概率分布定义的。高斯酉系综（GUE）描述了一类量子混沌哈密顿，而对应于泊松和高斯对角系综（GDE）的谱描述了非混沌的可积动力学。我们计算了量子多体系统分析中几类重要量的等谱旋转：框架势，Loschirt回声，OTOCS，纠缠，三方互信息，相干性，到平衡态的距离，量子电池中的工作和CP映射的扩展。此外，我们在这些合奏随机矩阵理论的平均值，并显示这些数量清楚地区分混沌量子动力学从非混沌的。
In this paper, we present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those defined by salient spectral probability distributions. The Gaussian Unitary Ensembles (GUE) describes a class of quantum chaotic Hamiltonians, while spectra corresponding to the Poisson and Gaussian Diagonal Ensemble (GDE) describe non chaotic, integrable dynamics. We compute the Isospectral twirling of several classes of important quantities in the analysis of quantum many-body systems: Frame potentials, Loschmidt Echos, OTOCS, Entanglement, Tripartite mutual information, coherence, distance to equilibrium states, work in quantum batteries and extension to CP-maps. Moreover, we perform averages in these ensembles by random matrix theory and show how these quantities clearly separate chaotic quantum dynamics from non chaotic ones.