Gaussian fluctuations from random Schrödinger equation

Abstract

We study the Schrödinger equation driven by a weak Brownian forcing, and derive Gaussian fluctuations in the form of a time-inhomogeneous Ornstein-Uhlenbeck process. As a result, when evaluated at a fixed frequency, the intensity of the incoherent wave is of exponential distribution.

v2, 26 pages, minor revision