发表机构
College of Science, National University of Defense Technology（国防科技大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对移动律随机-拟周期余圈，提出环境索引平稳射影族与环境匹配幺模群准则，证明在非紧致与强不可约条件下最大 Lyapunov 指数严格为正，并应用于随机-拟周期 Schrödinger 余圈。
AI 中文摘要
我们研究移动律随机环境矩阵余圈，其单步拟周期余圈律沿遍历环境轨道平稳变化。此时两种固定律结构不再充分：单一平稳射影测度不记录连续环境纤维之间的输运，而汇集移动支集可能产生沿任何环境轨道都不具有动态容许性的乘积。我们用环境索引的平稳射影族取代前者，并证明了环境方式的 Furstenberg 公式。当最大 Lyapunov 指数为零时，平均平稳性在支集层面升级为精确等变性，即 \\(g_*\eta^\omega=\eta^{\Theta\omega}\\)，这迫使要么存在环境方式的紧致约化，要么存在有限支集不变的由非零真可测子丛组成的族。因此，环境方式的非紧致性和环境方式的强不可约性蕴含正性。为解决第二个障碍，我们比较沿匹配环境段且具有相等总环面平移的容许乘积。因此它们的商是公共向量纤维上的真正回归，并生成环境匹配的幺模群。这些群的稳定非紧致性和稳定强不可约性验证了余圈级假设。将该框架应用于平稳变化的随机-拟周期 Schrödinger 余圈，在所述假设下，该框架在每一个实数能量处都产生最大 Lyapunov 指数的严格正性。
英文摘要
We study moving-law random-environment matrix cocycles whose one-step quasiperiodic cocycle law varies stationarily along an ergodic environment orbit. Two fixed-law structures then cease to suffice: a single stationary projective measure does not record transport between successive environment fibers, and pooling the moving supports may create products that are not dynamically admissible along any environment orbit. We replace the first by environment-indexed stationary projective families and prove an environment-wise Furstenberg formula. When the top Lyapunov exponent vanishes, averaged stationarity upgrades to exact equivariance at the support level, \(g_*η^ω=η^{Θω}\), which forces either an environment-wise compact reduction or a finite support-invariant family of nonzero proper measurable subbundles. Environment-wise noncompactness and environment-wise strong irreducibility therefore imply positivity. To address the second obstruction, we compare admissible products along matched environment segments with equal total torus translation. Thus their quotients are genuine returns on a common vector fiber and generate environment-matched monodromy groups. Stable noncompactness and stable strong irreducibility of these groups verify the cocycle-level hypotheses. Applied to stationarily varying random--quasiperiodic Schrödinger cocycles, the framework yields strict positivity of the top Lyapunov exponent at every real energy under the stated assumptions.
