发表机构
School of Mathematics & Physics, Yancheng Institute of Technology; School of Physics, Hubei University（盐城工学院数学与物理学院; 湖北大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过随机矩阵分析，研究随机自由费米子模型的热化，推导热化函数及其衰减，证明涨落消失，并建立弱ETH型自平均的可解模型。
AI 中文摘要
我们通过详细的随机矩阵分析研究了随机自由费米子模型中的热化。通过计算单粒子可观测量$A$的$\operatorname{Tr}(A\rho(t))$的系综平均和涨落，我们推导出热化函数$g^2(t/\tau_\lambda)$，其中$\tau_\lambda = \hbar/(2\eta\sqrt{N})$，证明了其$|t|^{-3}$渐近衰减，并表明在热力学极限下涨落的方差以$O(1/N)$阶消失。粒子数守恒也被纳入模型，由此我们进一步研究了能量壳本征态统计，并证明了本征态统计的因式分解定理。我们进一步表明，在受控的本征矢量-本征值关联形变下，对角能量分辨斜率与非对角本征态热化假设谱函数获得能量依赖结构。最后，我们计算了关联函数的涨落，并将其涨落尺度与完全混沌系统的涨落尺度进行比较，揭示了源于高斯性质的定量差异。这项工作确立了随机自由费米子模型作为弱本征态热化假设类型自平均的解析可解实现，以及作为本征基混沌可与谱混沌分离的可控设定。
英文摘要
We study the thermalization in the random free fermion model by a detailed random-matrix analysis. By computing the ensemble average and fluctuations of $\operatorname{Tr}(Aρ(t))$ for a single-particle observable $A$, we derive the thermalization function $g^2(t/τ_λ)$ with $τ_λ= \hbar/(2η\sqrt{N})$, prove its $|t|^{-3}$ asymptotic decay, and show that the variance of the fluctuations vanishes as $O(1/N)$ in the thermodynamic limit.Particle number conservation is also incorporated into the model, by which we further study the energy-shell eigenstate statistics and prove a factorization theorem of the eigenstate statistics. We further show that under a controlled eigenvector-eigenvalue correlation deformation, the diagonal energy-resolved slope and the off-diagonal eigenstate thermalization hypothesis spectral function acquire an energy dependence.Finally, we compute the fluctuations of correlation functions and compare the fluctuation scales with those of a fully chaotic system, revealing quantitative differences rooted in the Gaussian nature of the eigenstates.Our work establishes the random free fermion model as an analytically solvable realization of weak eigenstate thermalization hypothesis type self-averaging, and as a controllable setting in which eigenbasis chaos can be separated from spectral chaos.
Comments30 pages, 3 figures
