Wave propagation in non-Gaussian random media
Journal of Physics A: Mathematical and Theoretical 48 045206 (2015 )
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.
Keywords: waves, random media, field theory methods