Functional integral solution for wave propagation in random media

Abstract

Path integral formulation originated in quantum mechanics and probability theory and was widely used from the 1970s on to provide a formal solution to wave propagation in random media. The use of path integration arose because of the similarity of the parabolic approximation of the Helmholtz equation and the Schrodinger equation used in quantum mechanics. However, the inability to compute the path integral results lead only to asymptotic approximations. In the meantime, other methods—the multiple-phase screens and the multiple-scale expansion—were developed. These methods provided an approximation, valid though in-accurate, for arbitrary fluctuation strength. Later, researchers realized that the same results can be obained by using the configuration and phase space path integral procedures. Recently the interaction picture formulation, originated in quantum mechanics, provided an important link in the unification of all these procedures. It was shown that the approximations reached by the multiple-phase screens and the multiple-scale expansion methods are just crude approximations, valid for a thick phase screen. A surveyi of the functional solutions will be followed by a functional multiple-scale expansion formulation equivalent to the other functional solutions. If time will allow, computational aspects and open questions will be discussed.