= Wave propagation in a random medium
<Wave propagation in a random medium> studies how fluctuations of properties such as <refractive index>, <mass density> or <sound speed> change an incident <wave>. Different paths acquire different <wave phases>, and spatial inhomogeneities generate <wave scattering>. One realization can therefore show a complicated transmitted pattern even under simple illumination.
The <coherent field> $\langle u\rangle$ is the ensemble average of the field, while the <mean wave intensity> in a scalar normalization is $\langle|u|^2\rangle$. They obey
$$
\langle|u|^2\rangle=|\langle u\rangle|^2+\langle|u-\langle u\rangle|^2\rangle.
$$
Thus decay of the <coherent field> need not mean loss of total <wave energy>: randomized <wave phases> can transfer weight to fluctuating contributions. Comparing a phase-sensitive average with an average of detector <intensities> tests this distinction. Weak fluctuations can permit perturbation methods, whereas repeated <wave scattering> with retained <interference> can lead to <Anderson localization>.
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