Elastic wave transport in disordered, isotropic media: a supersymmetric sigma model

Starting from a continuum description of a disordered elastic medium, we have derived a supersymmetric field theoretic model enabling the prediction of ensemble average correlation functions that fully takes polarization effects into account. The model enables both perturbative and non-perturbative calculations in a similar fashion as corresponding models of disordered electronic systems. At intermediate distances, we show that a Hubbard-Stratonovic transformation can be carried out and obtain a supermatrix field theory. At distances far greater than the mean free paths of the system, we show that the action reduces to a nonlinear supersymmetric sigma model formally identical to that for a scalar field. Our results yield a bare diffusion constant given by a density of states weighted average of the classical diffusion constants of the coherent potential approximation(CPA) medium.