论文标题
在二维连续体中，弹性波的相干传播和不一致的扩散，边缘位错的随机分布
Coherent propagation and incoherent diffusion of elastic waves in a two dimensional continuum with a random distribution of edge dislocations
论文作者
论文摘要
我们研究了由许多随机放置和定向的边缘位错的二维连续体中平面弹性波的相干传播和不相干扩散。由于PEIERLS-NABARRO力，位错可以用频率$ω_0$绕平衡位置振荡。波和错位之间的耦合由桃子koehler力给出。这导致一个带有差异操作员的不均匀术语的波方程。在连贯的情况下，建立了质量运算符的dyson方程，并解决独立散射近似（ISA）中扰动理论中的所有顺序。结果，对于纵向和横向波，可以从中获得复杂的折射指数，从中可以读取效应波速度和衰减。在不连贯的情况下，建立了伯特 - 盐的方程式，并以低频和波数的极限求解在扰动理论中的领先顺序。获得扩散方程，并明确计算（频率依赖性的）扩散系数。它减少了以低频的能量传输参数获得的值。一个重要的中间步骤是获得涉及差分操作员的波方程的Ward-Takahashi身份（WTI），该方程与ISA兼容。
We study the coherent propagation and incoherent diffusion of in-plane elastic waves in a two dimensional continuum populated by many, randomly placed and oriented, edge dislocations. Because of the Peierls-Nabarro force the dislocations can oscillate around an equilibrium position with frequency $ω_0$. The coupling between waves and dislocations is given by the Peach-Koehler force. This leads to a wave equation with an inhomogeneous term that involves a differential operator. In the coherent case, a Dyson equation for a mass operator is set up and solved to all orders in perturbation theory in independent scattering approximation (ISA). As a result, a complex index of refraction is obtained, from which an effectve wave velocity and attenuation can be read off, for both longitudinal and transverse waves. In the incoherent case a Bethe-Salpeter equation is set up, and solved to leading order in perturbation theory in the limit of low frequency and wave number. A diffusion equation is obtained and the (frequency-dependent) diffusion coefficient is explicitly calculated. It reduces to the value obtained with energy transfer arguments at low frequency. An important intermediate step is the obtention of a Ward-Takahashi identity (WTI) for a wave equation that involves a differential operator, which is shown to be compatible with the ISA.
