Kinetic Limit for Wave Propagation in a Random Medium
Kinetic Limit for Wave Propagation in a Random Medium
复制标题
波在随机介质中传播的动力学极限
DOI：
10.1007/s00205-006-0005-9
复制
发表时间：
2005
影响因子：
2.5
通讯作者：
H. Spohn
中科院分区：
文献类型：
--
作者：
J. Lukkarinen;H. Spohn
我们在谐波近似下研究晶体动力学。原子质量是弱无序的，从某种意义上说，它们对均匀性的偏离是有序的
$$\sqrt{\epsilon}$$。色散关系被假定为莫尔斯函数并抑制交叉回忆。然后我们在极限中证明它
$$\epsilon\to 0$$，无序平均的维格纳函数在动力学尺度上，时间和空间上的有序
$$\epsilon^{-1}$$，由线性玻尔兹曼方程控制。
We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of the order
$$\sqrt{\epsilon}$$. The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit
$$\epsilon\to 0$$, the disorder-averaged Wigner function on the kinetic scale, time and space of order
$$\epsilon^{-1}$$, is governed by a linear Boltzmann equation.