Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect

Abstract

We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function and then study numerically the impact of time-correlated noise on the time evolution of a 1 + 1 dimensional generalized Langevin equation by comparing also to analytical results. Finally, we apply our method to the generalized Langevin equation with an external harmonic and double-well potential.

Comments: 11 pages, 12 figures; v2: Ref. [11] added, acknowledgments updated; v3: published version, additional results, 16 figures