微正则算子谱、BPS混沌与自由概率论
Microcanonical Operator Spectrum, BPS Chaos and Free Probability Theory
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中文总结 AI 辅助
本文研究混沌量子多体系统中简单算子投影到微正则能量窗口后的本征谱，证明在Haar随机基假设下其服从高斯随机矩阵统计，并探讨了对BPS混沌和本征态热化的影响。
中文摘要 AI 辅助
简单算子的矩阵元是混沌量子多体系统中热化的核心。它们的矩通常通过本征态热化假说进行统计描述。在本文中，我们研究这些矩阵元的一种更精细的表征：简单算子投影到微正则能量窗口后的本征谱。该谱一次性编码了矩阵元的所有矩，并且在哈密顿量谱简并时尤为重要。假设简单算子的本征基相对于哈密顿量的本征基是Haar随机取向的，我们证明投影到小微正则窗口的算子谱服从高斯随机矩阵统计。我们通过研究随机取向继承的概率分布以及使用自由概率论的工具直接证明了这一点。我们讨论了这对BPS混沌以及更一般的本征态热化的影响。
英文摘要
Matrix elements of simple operators are central to thermalization in chaotic quantum many-body systems. Their moments are often described statistically through the Eigenstate Thermalization Hypothesis. In this paper, we study a more refined characterization of these matrix elements: the eigenspectrum of simple operators once projected to microcanonical energy windows. The spectrum encodes all moments of the matrix elements at once, and is particularly relevant when the spectrum of the Hamiltonian is degenerate. Assuming that the eigenbasis of the simple operator is Haar-randomly oriented with respect to that of the Hamiltonian, we prove that the spectrum of an operator projected to a small microcanonical window obeys Gaussian random matrix statistics. We do this directly by studying the probability distribution inherited from the random orientation, as well as using tools from Free Probability Theory. We discuss the implications for BPS chaos and more generally for eigenstate thermalization.
发表机构
- Dipartimento di Fisica, Università di Milano - Bicocca（米兰比可卡大学物理系）
- INFN, sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）
- Department of Physics and Photon Science, Gwangju Institute of Science and Technology（光州科学技术院物理与光子科学系）
- Center for High Energy Physics, Peking University（北京大学高能物理中心）
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