Wave propagation in non-Gaussian random media

Abstract

We develop a compact perturbative series for acoustic wave propagation in a medium with a non-Gaussian stochastic speed of sound. We use Martin-Siggia and Rose auxiliary field techniques to render the classical wave propagation problem into a 'quantum' field theory one, and then frame this problem within the so-called Schwinger-Keldysh of closed time-path (CTP) formalism. Variation of the so-called two-particle irreducible (2PI) effective action (EA), whose arguments are both the mean fields and the irreducible two point correlations, yields the Schwinger-Dyson and the Bethe-Salpeter equations. We work out the loop expansion of the 2PI CTP EA and show that, in the paradigmatic problem of overlapping spherical intrusions in an otherwise homogeneous medium, non-Gaussian corrections might be much larger than Gaussian ones at the same order of loops.