S-matrices for waves in random structures, unitarization of diffuse field waveforms, and mesocopics

Abstract

Diffuse field methods, such as reverberation room acoustics and statistical energy analysis, predict wave energy flow in complex structures. These methods are applied here to predict the root mean square s‐matrix <s2(t)>1/2 for an undamped structure coupled to a single incoming and outgoing channel. Multiplying by a white noise random process produces a candidate s(t). The prediction is statistically exact if the internal scatterings are sufficiently phase incoherent, but it is not unitary and is thus inadmissible in the absence of such scatterings. Here it is shown that it can be made unitary in a minimally invasive manner by filtering with a minimum phase causal filter with modulus 1/|s(ω)|. This is illustrated with envelopes <s2(t)> predicated on a picture of the structure as a single reverberation room, as two coupled rooms, and as a quasi‐one dimensional multiply scattering system. The resulting unitarized S matrices are found to exhibit a variety of familiar mesoscopic features and behaviors not present in the original diffuse <s2(t)>. These include enhanced backscatter, quantum echo, power law tails, level repulsion, and Anderson localization. It is remarkable, and of potential practical interest, that quantitative mesoscopic features follow from simple principles. [Work supported by NSF CMS 05‐28096.]