水声传播的随机矩阵理论
Random matrix theory for underwater sound propagation
摘要：
海洋声传播可以用弱随机介质中的波导来描述，这种弱随机介质会产生多次散射。20年前，这被认为是一个量子混沌问题，但随机矩阵理论，量子或波混沌研究的支柱之一，从来没有被引入到这个问题中。波导的模式提供了传播的表示，其在抛物线近似中是么正的。由海洋内波引起的散射导致了一个幂律随机带状酉矩阵集合，用于远程深海声传播。该合奏有相似之处，但不同的，从那些研究安德森金属-绝缘体转变。由此产生的长程传播系综统计与使用抛物方程的全波传播的统计吻合得很好。
英文摘要：
Ocean acoustic propagation can be formulated as a wave guide with a weakly random medium generating multiple scattering. Twenty years ago, this was recognized as a quantum chaos problem, and yet random matrix theory, one pillar of quantum or wave chaos studies, has never been introduced into the subject. The modes of the wave guide provide a representation for the propagation, which in the parabolic approximation is unitary. Scattering induced by the ocean's internal waves leads to a power-law random banded unitary matrix ensemble for long-range deep ocean acoustic propagation. The ensemble has similarities, but differs, from those introduced for studying the Anderson metal-insulator transition. The resulting long-range propagation ensemble statistics agree well with those of full wave propagation using the parabolic equation.
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