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

TL;DR

This paper introduces an efficient simulation method for stationary Gaussian noise with arbitrary covariance, and investigates how time-correlated noise influences the dynamics of a generalized Langevin equation with various potentials.

Contribution

The paper develops a novel simulation approach for stationary Gaussian noise with arbitrary covariance functions and applies it to study the effects of correlated noise on Langevin dynamics.

Findings

Time-correlated noise significantly affects Langevin dynamics.

Simulation results align with analytical predictions.

Method enables studying complex noise effects in stochastic systems.

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.