关于任意复杂量子系统的矩阵系综

IF 5.4 1区 物理与天体物理 Q1 Physics and Astronomy
William E. Salazar, Juan Diego Urbina, Javier Madroñero
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引用次数: 0

摘要

我们对Deutsch[1,2]最初提出的特征向量集合的变化进行了全面的分析研究,以作为特征态热化假说(ETH)的基础。这个被称为c系综的系综包含了额外的系统相关信息,使复杂量子系统的研究超越了随机矩阵理论(RMT)的普遍预测。具体地说,我们关注于系统特定的细节如何影响相关函数中的后期行为,例如谱形式因子,以及如何包括RMT未捕获的显式哈密顿校正。我们通过证明它定义任意系统的幺正1设计和强混沌系统的近似2设计,证明了该系综相对于泛(Haar)结果的一致性。导出了两点和四点集成平均相关函数的通用表达式,揭示了系统相关信息是如何频谱解耦的。此外,我们表明,对于小能量窗口,由该系综定义的相关函数减少到ETH所做的预测。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On a matrix ensemble for arbitrary complex quantum systems

We present a comprehensive analytical study of a variation of the eigenvector ensemble initially proposed by Deutsch [1, 2] for the foundations of the Eigenstate Thermalization Hypothesis (ETH). This ensemble, called the C-ensemble, incorporates additional system-dependent information, enabling the study of complex quantum systems beyond the universal predictions of Random Matrix Theory (RMT). Specifically, we focus on how system-specific details influence late-time behavior in correlation functions, such as the spectral form factor, and how explicit Hamiltonian corrections not captured by RMT can be included. We demonstrate the consistency of this ensemble with respect to the universal (Haar) results by showing that it defines a unitary 1-design for arbitrary systems and for strongly chaotic systems it becomes an approximated 2-design. Universal expressions for two- and four-point ensemble-averaged correlation functions are derived, revealing how system-dependent information is spectrally decoupled. Furthermore, we show that for small energy windows, the correlation functions defined by this ensemble reduce to the predictions made by the ETH.

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来源期刊
Journal of High Energy Physics
Journal of High Energy Physics 物理-物理:粒子与场物理
CiteScore
10.30
自引率
46.30%
发文量
2107
审稿时长
1.5 months
期刊介绍: The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal. Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles. JHEP presently encompasses the following areas of theoretical and experimental physics: Collider Physics Underground and Large Array Physics Quantum Field Theory Gauge Field Theories Symmetries String and Brane Theory General Relativity and Gravitation Supersymmetry Mathematical Methods of Physics Mostly Solvable Models Astroparticles Statistical Field Theories Mostly Weak Interactions Mostly Strong Interactions Quantum Field Theory (phenomenology) Strings and Branes Phenomenological Aspects of Supersymmetry Mostly Strong Interactions (phenomenology).
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