Wave propagation in non Gaussian random media

Abstract

We develop a compact perturbative series for accoustic 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 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 may be much larger than Gaussian ones at the same order of loops