AI 中文总结
该研究在林德布拉德晶格动力学中构建量子图灵斑图，建立其严格理论，揭示量子纠缠与波长选择的关联，数值模拟呈现多种斑图形态。
AI 中文摘要
我们在林德布拉德晶格动力学中构建量子图灵斑图，并建立其非线性阶与量子涨落的严格理论。对于具有有限范围耦合的显式完全正族，一阶矩方程在非零波数处经历超临界不稳定性，且存在解析的位点中心和键中心的共振条纹分支。这些分支在其反射固定周期单元空间中局部渐近稳定，投影相干态在半经典极限下的每个有界时间区间上展现出广泛的布拉格序。我们证明微观协方差以$O(N^{-1/2})$的速率收敛到非自治高斯李雅普诺夫流，将严格的部分转置不确定性违反转移到足够大的$N$。在均匀高斯区域，单一无量纲比率同时控制图灵稳定性行列式和相反动量的对数负性，将波长选择直接与量子纠缠关联起来。差分输运将最强的相反动量相关性从红外转移到选定的图灵尺度。数值延拓和二维模拟显示出条纹、斑点和迷宫形态，其傅里叶模式和涨落谱集中在相同的选定波数上。
英文摘要
We construct quantum Turing patterns in Lindblad lattice dynamics and establish a rigorous theory of their nonlinear order and quantum fluctuations. For an explicit family of completely positive lattice generators with finite-range couplings, the first-moment equations undergo a supercritical instability at a nonzero wave number and admit analytic site- and bond-centered commensurate stripe branches. These branches are locally asymptotically stable in their reflection-fixed period-cell spaces, and projected coherent states exhibit extensive Bragg order on every bounded time interval in the semiclassical limit. We prove $O(N^{-1/2})$ convergence of microscopic covariances to a nonautonomous Gaussian Lyapunov flow, transferring strict partial-transpose uncertainty violations to sufficiently large $N$. In the homogeneous Gaussian sector, a single dimensionless ratio controls both the Turing stability determinant and the logarithmic negativity of opposite momenta, relating wavelength selection directly to quantum entanglement. Differential transport shifts the strongest opposite-momentum correlations from the infrared to the selected Turing scale. Numerical continuation and two-dimensional simulations display stripe, spot, and labyrinth morphologies whose Fourier modes and fluctuation spectra concentrate at the same selected wave numbers.
CommentsCode, data and Lean 4 formalization are available in https://github.com/IKEDAKAZUKI/Quantum-Turing-Pattern
