来自涨落量子视界的谱混沌
Spectral Chaos from a Fluctuating Quantum Horizon
- National Tsing-Hua University（国立清华大学）
- Center for Theory-Computation-Data Science Research, National Tsing-Hua University（国立清华大学理论计算数据科学研究中⼼）
- National Center for Theoretical Sciences（国家理论科学中⼼）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明视界矩阵模型中模糊球几何的量子涨落解除部分子简并，生成具有结构化协方差的哈密顿量系综，其谱呈现GOE/GUE/GSE及Pandey-Mehta交叉，为黑洞谱混沌提供微观基础。
AI中文摘要：
黑洞被推测是最大混沌的，其量子谱预期表现出普遍的随机矩阵关联。然而，这一预期迄今为止主要依赖于全息描述或许多体模型，在这些模型中随机性是被引入的，而非从视界本身的微观自由度推导出来的。在视界矩阵模型中，模糊球支持高度简并的部分子态，其多重性解释了黑洞熵。我们证明，视界几何的量子涨落会解除这种简并，并生成一个单部分子哈密顿量系综。该系综的算子结构和秩依赖协方差均由微观模型决定，而非由淬火耦合固定。尽管协方差具有这种结构，所得谱仍表现出由其反幺正对称类决定的GOE、GUE和GSE统计，且相邻能隙统计量随矩阵尺寸增大而日益自平均。该模型还实现了普遍的Pandey-Mehta正交-幺正交叉，交叉尺度由微观几何协方差决定。秩分辨方差分析表明，涨落强度在张量秩上直至微观截断处仍广泛分布，为观察到的Wigner-Dyson普遍性和有效非局域动力学提供了微观基础。反幺正对称性直接作用于模糊球几何，因此条件哈密顿量的Dyson类由底层量子几何的反幺正对称性决定。这为JT引力中几何与随机矩阵普遍性之间的Stanford-Witten关系提供了微观对应。这些结果建立了从量子视界几何到黑洞谱混沌的微观途径。
英文摘要：
Black holes are conjectured to be maximally chaotic, with their quantum spectra expected to exhibit universal random-matrix correlations. This expectation, however, has so far rested largely on holographic descriptions or on many-body models in which randomness is introduced rather than derived from the microscopic degrees of freedom of the horizon itself. In the horizon matrix model, the fuzzy sphere supports highly degenerate parton states whose multiplicity accounts for the black-hole entropy. We show that quantum fluctuations of the horizon geometry lift this degeneracy and generate an ensemble of one-parton Hamiltonians. Both the operator structure and the rank-dependent covariance of this ensemble are determined by the microscopic model, rather than fixed by quenched couplings. Despite this structured covariance, the resulting spectra exhibit GOE, GUE, and GSE statistics dictated by their antiunitary symmetry classes, with the adjacent-gap statistic becoming increasingly self-averaging with matrix size. The model also realizes the universal Pandey--Mehta orthogonal-to-unitary crossover, with the crossover scale determined by the microscopic geometric covariance. A rank-resolved variance analysis shows that the fluctuation strength remains broadly distributed across tensor ranks up to the microscopic cutoff, providing a microscopic basis for the observed Wigner--Dyson universality and effectively nonlocal dynamics. The antiunitary symmetry acts directly on the fuzzy-sphere geometry, so the Dyson class of a conditional Hamiltonian is determined by the antiunitary symmetry of the underlying quantum geometry. This provides a microscopic counterpart of the Stanford--Witten relation between geometry and random-matrix universality in JT gravity. These results establish a microscopic route from quantum horizon geometry to black-hole spectral chaos.
