FORWARD AND MARKOV APPROXIMATION - THE STRONG-INTENSITY-FLUCTUATIONS REGIME REVISITED

The forward and Markov approximation for high-frequency waves propagat ing in weakly fluctuating random media is the solution of a stochastic Schrodinger equation. In this context, the strong-intensity-fluctuati ons regime corresponds to long propagation distances. This regime has been studied by several different methods, such as expansion of the mo ment equations and path-integral representations. It is an accepted fa ct that, in this regime, the field becomes Gaussian and completely dec orrelated which implies, in particular, that the intensity has an expo nential probability distribution. The aim of this paper is to give add itional evidence for this by analysing the stationary moment equations . Under the natural hypothesis of asymptotic spatial decorrelation of the field, we construct boundary conditions for these stationary equat ions which can then be solved explicitly. We note that the limiting pr obability distribution does not depend on the spectral content of the randomness, which plays an essential role at finite propagation distan ces in the regime of saturation of the intensity fluctuations. Our ana lysis deals with the long-distance, equilibrium behaviour of the stati stics of the intensity without having to deal with the approach to equ ilibrium.