Long-time asymptotic of temporal-spatial coherence function for light propagation through time dependent disorder

Abstract

The long-time asymptote of the field autocorrelation function for radiation propagated through a medium of point-like scatterers is studied using the Bethe-Salpeter equation. It is shown that for a plane source the fluctuation intensity (the zeroth spatial moment of the correlator) damps out following a power-logarithmically stretched exponential decay law, the exponent and preexponent being dependent on the scattering angle. The spatial center of gravity and dispersion of the correlator (the normalized first and second moments, respectively) turn out to be to weakly divergent at infinite time. A spin analogy of this problem is also discussed.