发表机构
[W.\ Liu] Department of Mathematics, Texas A\&M University, College Station, TX 77843, USA; [X.\ Wang] Department of Mathematics, Texas A\&M University, College Station, TX 77843, USA（; ）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对带偶势的单频拟周期薛定谔算子，证明其量子动力学的对数尺度及矩阶数依赖均为尖锐值，通过适配双局域中心的反射型半一致局域本征函数得到时间序列的对数下界。
AI 中文摘要
动力学局域化要求量子波包的所有位置矩在时间上保持有界，但对于拟周期薛定谔算子，这类界通常在相位上不具有一致性。在正李雅普诺夫指数区域，目前已知的最佳相位一致估计却以对数尺度增长。我们针对一类带有偶势的单频拟周期薛定谔算子，证明了对数尺度以及对矩阶数的依赖都是尖锐的。我们的主要方法是半一致局域本征函数的反射版本，该版本适配了由完全共振相位强制产生的两个局域中心，由此我们得到了沿时间序列的匹配对数下界。
英文摘要
Dynamical localization requires all position moments of a quantum wavepacket to remain bounded in time, but for quasiperiodic Schrödinger operators such bounds are generally not uniform in phase. In the positive Lyapunov exponent regime, the best known phase-uniform estimates instead grow on a logarithmic scale. We prove that both the logarithmic scale and the dependence on the moment order are sharp for a class of one-frequency quasiperiodic Schrödinger operators with even potentials. Our main ingredient is a reflective version of semi-uniformly localized eigenfunctions, adapted to the two localization centers forced by a completely resonant phase, from which we obtain matching logarithmic lower bounds along sequences of times.
Comments34 pages, comments welcome!
