Generation of Colored Noise

In this work, we describe a simple Markovian algorithm to generate a typical sample path of colored noise described by an Ornstein–Uhlenbeck process. The algorithm works equally well to simulate a real or complex disorder potential with exponentially decaying covariance and higher correlation functions given by Wick's theorem. As an input, we only need independent Gaussian random numbers which can easily be generated by the well-known Box–Muller algorithm. Finally, we discuss an alternative method which can also be used to generate non-Gaussian colored noise.