调和近似下晶格动力学的局部平稳性
Local stationarity for lattice dynamics in the harmonic approximation
摘要：
本文在调和近似下研究了具有任意单胞的简单超立方晶格的晶格动力学。初始数据根据概率测量是随机的，该概率测量在线性尺度$ε^{-1}$上强制缓慢的空间变化。我们建立了两个时间机制。对于阶数为$ε^{-γ}$、$0<γ<1$的时间，该测度局部地收敛于高斯测度，该高斯测度是时空平稳的，具有从初始（一般而言，非高斯）测度继承的协方差。对于时间的顺序$ε^{-1}$，这种局部空间协方差随时间变化，并由一个半经典输运方程。
英文摘要：
We consider the lattice dynamics in the harmonic approximation for We consider the lattice dynamics in the harmonic approximation for a simple hypercubic lattice with arbitrary unit cell. The initial data are random according to a probability measure which enforces slow spatial variation on the linear scale $ε^{-1}$. We establish two time regimes. For times of order $ε^{-γ}$, $0<γ<1$, locally the measure converges to a Gaussian measure which is space-time stationary with a covariance inherited from the initial (in general, non-Gaussian) measure. For times of order $ε^{-1}$ this local space covariance changes in time and is governed by a semiclassical transport equation.
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