Samelsohn Gregory, Freilikher Valentin, Haridim Motti
Department of Communication Engineering, Holon Institute of Technology, Holon 58102, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 2):066602. doi: 10.1103/PhysRevE.78.066602. Epub 2008 Dec 3.
An original approach is developed for the description of spectral coherence and time-domain transport of wave fields scattered in random media. This approach accounts explicitly for the correlation properties of the disorder and is universal with respect to the dimensionality of the system. Specifically, a two-frequency mutual coherence function is evaluated by using a procedure of embedding the initial Helmholtz equation into an auxiliary problem of a directed wave propagating in a higher-dimensional space. The resulting Schrödinger-like equation is solved perturbatively by means of a cumulant path integral technique. Mean intensity profiles and temporal moments of a narrowband wave packet scattered in a random medium are calculated by using the Fourier transformation of the coherence function. The theory describes the ballistic to diffusive transition in wave transport, and is consistent with experimental results. Since the coherence function is expressed via an arbitrary form power spectrum, the results obtained open a new avenue for studying wave transport in anisotropic and/or fractally correlated systems.
本文提出了一种新颖的方法，用于描述随机介质中散射波场的光谱相干性和时域传输特性。该方法明确考虑了无序的相关特性，并且对于系统的维度具有通用性。具体而言，通过将初始亥姆霍兹方程嵌入到高维空间中定向波传播的辅助问题的过程，来评估双频互相关函数。所得的类薛定谔方程通过累积量路径积分技术进行微扰求解。利用相干函数的傅里叶变换，计算了随机介质中散射窄带波包的平均强度分布和时间矩。该理论描述了波传输中的弹道到扩散的转变，并且与实验结果一致。由于相干函数是通过任意形式的功率谱来表示的，因此所获得的结果为研究各向异性和/或分形相关系统中的波传输开辟了一条新途径。
