Colored Noise in Dynamical Systems

Large dynamical systems that possess a clear separation of time scales in their degrees of freedom can be simplified by “projecting out” the fast variables as noise. If these noise terms are uncorrelated in time (also referred to as white noise), Markovian stochastic processes can be used to study such systems which are relatively easier to work with. However, real systems are typically driven by correlated fluctuations and we need to use more sophisticated tools to deal with this so-called colored noise. In this talk, we will discuss how to work with such Non-Markovian systems, specifically those that are in contact with a heat bath and can be described by the Generalized Langevin Equation.