Title: Propagating wave correlations in complex systems,
Abstract: We describe a novel approach for computing wave correlation functions inside
finite spatial domains driven by complex and statistical sources. By exploiting
semiclassical approximations, we provide explicit algorithms to calculate the
local mean of these correlation functions in terms of the underlying classical
dynamics. By defining appropriate ensemble averages, we show that fluctuations
about the mean can be characterised in terms of classical correlations. We give
in particular an explicit expression relating fluctuations of diagonal
contributions to those of the full wave correlation function. The methods have
a wide range of applications both in quantum mechanics and for classical wave
problems such as in vibro-acoustics and electromagnetism. We apply the methods
here to simple quantum systems, so-called quantum maps, which model the
behaviour of generic problems on Poincaré sections. Although low-dimensional,
these models exhibit a chaotic classical limit and share common characteristics
with wave propagation in complex structures.